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Translate the given Common_Lisp code snippet into Go without altering its behavior.
(defun factorial (n) (if (< n 2) 1 (* n (factorial (1- n)))) ) (defun primep (n) "Primality test using Wilson's Theorem" (unless (zerop n) (zerop (mod (1+ (factorial (1- n))) n)) ))
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Rewrite the snippet below in C so it works the same as the original D code.
import std.bigint; import std.stdio; BigInt fact(long n) { BigInt f = 1; for (int i = 2; i <= n; i++) { f *= i; } return f; } bool isPrime(long p) { if (p <= 1) { return false; } return (fact(p - 1) + 1) % p == 0; } void main() { writeln("Primes less than 100 testing by Wilson's Theorem"); foreach (i; 0 .. 101) { if (isPrime(i)) { write(i, ' '); } } writeln; }
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Keep all operations the same but rewrite the snippet in C#.
import std.bigint; import std.stdio; BigInt fact(long n) { BigInt f = 1; for (int i = 2; i <= n; i++) { f *= i; } return f; } bool isPrime(long p) { if (p <= 1) { return false; } return (fact(p - 1) + 1) % p == 0; } void main() { writeln("Primes less than 100 testing by Wilson's Theorem"); foreach (i; 0 .. 101) { if (isPrime(i)) { write(i, ' '); } } writeln; }
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Can you help me rewrite this code in C++ instead of D, keeping it the same logically?
import std.bigint; import std.stdio; BigInt fact(long n) { BigInt f = 1; for (int i = 2; i <= n; i++) { f *= i; } return f; } bool isPrime(long p) { if (p <= 1) { return false; } return (fact(p - 1) + 1) % p == 0; } void main() { writeln("Primes less than 100 testing by Wilson's Theorem"); foreach (i; 0 .. 101) { if (isPrime(i)) { write(i, ' '); } } writeln; }
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Generate an equivalent Java version of this D code.
import std.bigint; import std.stdio; BigInt fact(long n) { BigInt f = 1; for (int i = 2; i <= n; i++) { f *= i; } return f; } bool isPrime(long p) { if (p <= 1) { return false; } return (fact(p - 1) + 1) % p == 0; } void main() { writeln("Primes less than 100 testing by Wilson's Theorem"); foreach (i; 0 .. 101) { if (isPrime(i)) { write(i, ' '); } } writeln; }
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Transform the following D implementation into Python, maintaining the same output and logic.
import std.bigint; import std.stdio; BigInt fact(long n) { BigInt f = 1; for (int i = 2; i <= n; i++) { f *= i; } return f; } bool isPrime(long p) { if (p <= 1) { return false; } return (fact(p - 1) + 1) % p == 0; } void main() { writeln("Primes less than 100 testing by Wilson's Theorem"); foreach (i; 0 .. 101) { if (isPrime(i)) { write(i, ' '); } } writeln; }
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Transform the following D implementation into Go, maintaining the same output and logic.
import std.bigint; import std.stdio; BigInt fact(long n) { BigInt f = 1; for (int i = 2; i <= n; i++) { f *= i; } return f; } bool isPrime(long p) { if (p <= 1) { return false; } return (fact(p - 1) + 1) % p == 0; } void main() { writeln("Primes less than 100 testing by Wilson's Theorem"); foreach (i; 0 .. 101) { if (isPrime(i)) { write(i, ' '); } } writeln; }
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Generate a C translation of this Erlang snippet without changing its computational steps.
#! /usr/bin/escript isprime(N) when N < 2 -> false; isprime(N) when N band 1 =:= 0 -> N =:= 2; isprime(N) -> fac_mod(N - 1, N) =:= N - 1. fac_mod(N, M) -> fac_mod(N, M, 1). fac_mod(1, _, A) -> A; fac_mod(N, M, A) -> fac_mod(N - 1, M, A*N rem M). main(_) -> io:format("The first few primes (via Wilson's theorem) are: ~n~p~n", [[K || K <- lists:seq(1, 128), isprime(K)]]).
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Write a version of this Erlang function in C# with identical behavior.
#! /usr/bin/escript isprime(N) when N < 2 -> false; isprime(N) when N band 1 =:= 0 -> N =:= 2; isprime(N) -> fac_mod(N - 1, N) =:= N - 1. fac_mod(N, M) -> fac_mod(N, M, 1). fac_mod(1, _, A) -> A; fac_mod(N, M, A) -> fac_mod(N - 1, M, A*N rem M). main(_) -> io:format("The first few primes (via Wilson's theorem) are: ~n~p~n", [[K || K <- lists:seq(1, 128), isprime(K)]]).
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Write the same code in C++ as shown below in Erlang.
#! /usr/bin/escript isprime(N) when N < 2 -> false; isprime(N) when N band 1 =:= 0 -> N =:= 2; isprime(N) -> fac_mod(N - 1, N) =:= N - 1. fac_mod(N, M) -> fac_mod(N, M, 1). fac_mod(1, _, A) -> A; fac_mod(N, M, A) -> fac_mod(N - 1, M, A*N rem M). main(_) -> io:format("The first few primes (via Wilson's theorem) are: ~n~p~n", [[K || K <- lists:seq(1, 128), isprime(K)]]).
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Write the same code in Java as shown below in Erlang.
#! /usr/bin/escript isprime(N) when N < 2 -> false; isprime(N) when N band 1 =:= 0 -> N =:= 2; isprime(N) -> fac_mod(N - 1, N) =:= N - 1. fac_mod(N, M) -> fac_mod(N, M, 1). fac_mod(1, _, A) -> A; fac_mod(N, M, A) -> fac_mod(N - 1, M, A*N rem M). main(_) -> io:format("The first few primes (via Wilson's theorem) are: ~n~p~n", [[K || K <- lists:seq(1, 128), isprime(K)]]).
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Change the programming language of this snippet from Erlang to Python without modifying what it does.
#! /usr/bin/escript isprime(N) when N < 2 -> false; isprime(N) when N band 1 =:= 0 -> N =:= 2; isprime(N) -> fac_mod(N - 1, N) =:= N - 1. fac_mod(N, M) -> fac_mod(N, M, 1). fac_mod(1, _, A) -> A; fac_mod(N, M, A) -> fac_mod(N - 1, M, A*N rem M). main(_) -> io:format("The first few primes (via Wilson's theorem) are: ~n~p~n", [[K || K <- lists:seq(1, 128), isprime(K)]]).
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Convert this Erlang snippet to Go and keep its semantics consistent.
#! /usr/bin/escript isprime(N) when N < 2 -> false; isprime(N) when N band 1 =:= 0 -> N =:= 2; isprime(N) -> fac_mod(N - 1, N) =:= N - 1. fac_mod(N, M) -> fac_mod(N, M, 1). fac_mod(1, _, A) -> A; fac_mod(N, M, A) -> fac_mod(N - 1, M, A*N rem M). main(_) -> io:format("The first few primes (via Wilson's theorem) are: ~n~p~n", [[K || K <- lists:seq(1, 128), isprime(K)]]).
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Generate an equivalent C version of this F# code.
let wP(n,g)=(n+1I)%g=0I let fN=Seq.unfold(fun(n,g)->Some((n,g),((n*g),(g+1I))))(1I,2I)|>Seq.filter wP fN|>Seq.take 120|>Seq.iter(fun(_,n)->printf "%A " n);printfn "\n" fN|>Seq.skip 999|>Seq.take 15|>Seq.iter(fun(_,n)->printf "%A " n);printfn ""
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Transform the following F# implementation into C#, maintaining the same output and logic.
let wP(n,g)=(n+1I)%g=0I let fN=Seq.unfold(fun(n,g)->Some((n,g),((n*g),(g+1I))))(1I,2I)|>Seq.filter wP fN|>Seq.take 120|>Seq.iter(fun(_,n)->printf "%A " n);printfn "\n" fN|>Seq.skip 999|>Seq.take 15|>Seq.iter(fun(_,n)->printf "%A " n);printfn ""
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Generate an equivalent C++ version of this F# code.
let wP(n,g)=(n+1I)%g=0I let fN=Seq.unfold(fun(n,g)->Some((n,g),((n*g),(g+1I))))(1I,2I)|>Seq.filter wP fN|>Seq.take 120|>Seq.iter(fun(_,n)->printf "%A " n);printfn "\n" fN|>Seq.skip 999|>Seq.take 15|>Seq.iter(fun(_,n)->printf "%A " n);printfn ""
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Translate the given F# code snippet into Java without altering its behavior.
let wP(n,g)=(n+1I)%g=0I let fN=Seq.unfold(fun(n,g)->Some((n,g),((n*g),(g+1I))))(1I,2I)|>Seq.filter wP fN|>Seq.take 120|>Seq.iter(fun(_,n)->printf "%A " n);printfn "\n" fN|>Seq.skip 999|>Seq.take 15|>Seq.iter(fun(_,n)->printf "%A " n);printfn ""
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Preserve the algorithm and functionality while converting the code from F# to Python.
let wP(n,g)=(n+1I)%g=0I let fN=Seq.unfold(fun(n,g)->Some((n,g),((n*g),(g+1I))))(1I,2I)|>Seq.filter wP fN|>Seq.take 120|>Seq.iter(fun(_,n)->printf "%A " n);printfn "\n" fN|>Seq.skip 999|>Seq.take 15|>Seq.iter(fun(_,n)->printf "%A " n);printfn ""
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Translate the given F# code snippet into Go without altering its behavior.
let wP(n,g)=(n+1I)%g=0I let fN=Seq.unfold(fun(n,g)->Some((n,g),((n*g),(g+1I))))(1I,2I)|>Seq.filter wP fN|>Seq.take 120|>Seq.iter(fun(_,n)->printf "%A " n);printfn "\n" fN|>Seq.skip 999|>Seq.take 15|>Seq.iter(fun(_,n)->printf "%A " n);printfn ""
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Keep all operations the same but rewrite the snippet in C.
USING: formatting grouping io kernel lists lists.lazy math math.factorials math.functions prettyprint sequences ; : wilson ( n -- ? ) [ 1 - factorial 1 + ] [ divisor? ] bi ; : prime? ( n -- ? ) dup 2 < [ drop f ] [ wilson ] if ; : primes ( -- list ) 1 lfrom [ prime? ] lfilter ; "n prime?\n--- -----" print { 2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 } [ dup prime? "%-3d %u\n" printf ] each nl "First 120 primes via Wilson's theorem:" print 120 primes ltake list>array 20 group simple-table. nl "1000th through 1015th primes:" print 16 primes 999 [ cdr ] times ltake list>array [ pprint bl ] each nl
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Convert this Factor block to C#, preserving its control flow and logic.
USING: formatting grouping io kernel lists lists.lazy math math.factorials math.functions prettyprint sequences ; : wilson ( n -- ? ) [ 1 - factorial 1 + ] [ divisor? ] bi ; : prime? ( n -- ? ) dup 2 < [ drop f ] [ wilson ] if ; : primes ( -- list ) 1 lfrom [ prime? ] lfilter ; "n prime?\n--- -----" print { 2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 } [ dup prime? "%-3d %u\n" printf ] each nl "First 120 primes via Wilson's theorem:" print 120 primes ltake list>array 20 group simple-table. nl "1000th through 1015th primes:" print 16 primes 999 [ cdr ] times ltake list>array [ pprint bl ] each nl
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Maintain the same structure and functionality when rewriting this code in C++.
USING: formatting grouping io kernel lists lists.lazy math math.factorials math.functions prettyprint sequences ; : wilson ( n -- ? ) [ 1 - factorial 1 + ] [ divisor? ] bi ; : prime? ( n -- ? ) dup 2 < [ drop f ] [ wilson ] if ; : primes ( -- list ) 1 lfrom [ prime? ] lfilter ; "n prime?\n--- -----" print { 2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 } [ dup prime? "%-3d %u\n" printf ] each nl "First 120 primes via Wilson's theorem:" print 120 primes ltake list>array 20 group simple-table. nl "1000th through 1015th primes:" print 16 primes 999 [ cdr ] times ltake list>array [ pprint bl ] each nl
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Produce a functionally identical Java code for the snippet given in Factor.
USING: formatting grouping io kernel lists lists.lazy math math.factorials math.functions prettyprint sequences ; : wilson ( n -- ? ) [ 1 - factorial 1 + ] [ divisor? ] bi ; : prime? ( n -- ? ) dup 2 < [ drop f ] [ wilson ] if ; : primes ( -- list ) 1 lfrom [ prime? ] lfilter ; "n prime?\n--- -----" print { 2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 } [ dup prime? "%-3d %u\n" printf ] each nl "First 120 primes via Wilson's theorem:" print 120 primes ltake list>array 20 group simple-table. nl "1000th through 1015th primes:" print 16 primes 999 [ cdr ] times ltake list>array [ pprint bl ] each nl
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Translate this program into Python but keep the logic exactly as in Factor.
USING: formatting grouping io kernel lists lists.lazy math math.factorials math.functions prettyprint sequences ; : wilson ( n -- ? ) [ 1 - factorial 1 + ] [ divisor? ] bi ; : prime? ( n -- ? ) dup 2 < [ drop f ] [ wilson ] if ; : primes ( -- list ) 1 lfrom [ prime? ] lfilter ; "n prime?\n--- -----" print { 2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 } [ dup prime? "%-3d %u\n" printf ] each nl "First 120 primes via Wilson's theorem:" print 120 primes ltake list>array 20 group simple-table. nl "1000th through 1015th primes:" print 16 primes 999 [ cdr ] times ltake list>array [ pprint bl ] each nl
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Transform the following Factor implementation into Go, maintaining the same output and logic.
USING: formatting grouping io kernel lists lists.lazy math math.factorials math.functions prettyprint sequences ; : wilson ( n -- ? ) [ 1 - factorial 1 + ] [ divisor? ] bi ; : prime? ( n -- ? ) dup 2 < [ drop f ] [ wilson ] if ; : primes ( -- list ) 1 lfrom [ prime? ] lfilter ; "n prime?\n--- -----" print { 2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 } [ dup prime? "%-3d %u\n" printf ] each nl "First 120 primes via Wilson's theorem:" print 120 primes ltake list>array 20 group simple-table. nl "1000th through 1015th primes:" print 16 primes 999 [ cdr ] times ltake list>array [ pprint bl ] each nl
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Produce a functionally identical C code for the snippet given in Forth.
: fac-mod >r 1 swap begin dup 0> while dup rot * r@ mod swap 1- repeat drop rdrop ; : ?prime dup 1- tuck swap fac-mod = ; : .primes cr 2 ?do i ?prime if i . then loop ;
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Port the following code from Forth to C# with equivalent syntax and logic.
: fac-mod >r 1 swap begin dup 0> while dup rot * r@ mod swap 1- repeat drop rdrop ; : ?prime dup 1- tuck swap fac-mod = ; : .primes cr 2 ?do i ?prime if i . then loop ;
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Can you help me rewrite this code in C++ instead of Forth, keeping it the same logically?
: fac-mod >r 1 swap begin dup 0> while dup rot * r@ mod swap 1- repeat drop rdrop ; : ?prime dup 1- tuck swap fac-mod = ; : .primes cr 2 ?do i ?prime if i . then loop ;
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Produce a functionally identical Java code for the snippet given in Forth.
: fac-mod >r 1 swap begin dup 0> while dup rot * r@ mod swap 1- repeat drop rdrop ; : ?prime dup 1- tuck swap fac-mod = ; : .primes cr 2 ?do i ?prime if i . then loop ;
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Translate the given Forth code snippet into Python without altering its behavior.
: fac-mod >r 1 swap begin dup 0> while dup rot * r@ mod swap 1- repeat drop rdrop ; : ?prime dup 1- tuck swap fac-mod = ; : .primes cr 2 ?do i ?prime if i . then loop ;
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Translate the given Haskell code snippet into C without altering its behavior.
import qualified Data.Text as T import Data.List main = do putStrLn $ showTable True ' ' '-' ' ' $ ["p","isPrime"]:map (\p -> [show p, show $ isPrime p]) numbers putStrLn $ "The first 120 prime numbers are:" putStrLn $ see 20 $ take 120 primes putStrLn "The 1,000th to 1,015th prime numbers are:" putStrLn $ see 16.take 16 $ drop 999 primes numbers = [2,3,9,15,29,37,47,57,67,77,87,97,237,409,659] primes = [p | p <- 2:[3,5..], isPrime p] isPrime :: Integer -> Bool isPrime p = if p < 2 then False else 0 == mod (succ $ product [1..pred p]) p bagOf :: Int -> [a] -> [[a]] bagOf _ [] = [] bagOf n xs = let (us,vs) = splitAt n xs in us : bagOf n vs see :: Show a => Int -> [a] -> String see n = unlines.map unwords.bagOf n.map (T.unpack.T.justifyRight 3 ' '.T.pack.show) showTable::Bool -> Char -> Char -> Char -> [[String]] -> String showTable _ _ _ _ [] = [] showTable header ver hor sep contents = unlines $ hr:(if header then z:hr:zs else intersperse hr zss) ++ [hr] where vss = map (map length) $ contents ms = map maximum $ transpose vss ::[Int] hr = concatMap (\ n -> sep : replicate n hor) ms ++ [sep] top = replicate (length hr) hor bss = map (\ps -> map (flip replicate ' ') $ zipWith (-) ms ps) $ vss zss@(z:zs) = zipWith (\us bs -> (concat $ zipWith (\x y -> (ver:x) ++ y) us bs) ++ [ver]) contents bss
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Preserve the algorithm and functionality while converting the code from Haskell to C#.
import qualified Data.Text as T import Data.List main = do putStrLn $ showTable True ' ' '-' ' ' $ ["p","isPrime"]:map (\p -> [show p, show $ isPrime p]) numbers putStrLn $ "The first 120 prime numbers are:" putStrLn $ see 20 $ take 120 primes putStrLn "The 1,000th to 1,015th prime numbers are:" putStrLn $ see 16.take 16 $ drop 999 primes numbers = [2,3,9,15,29,37,47,57,67,77,87,97,237,409,659] primes = [p | p <- 2:[3,5..], isPrime p] isPrime :: Integer -> Bool isPrime p = if p < 2 then False else 0 == mod (succ $ product [1..pred p]) p bagOf :: Int -> [a] -> [[a]] bagOf _ [] = [] bagOf n xs = let (us,vs) = splitAt n xs in us : bagOf n vs see :: Show a => Int -> [a] -> String see n = unlines.map unwords.bagOf n.map (T.unpack.T.justifyRight 3 ' '.T.pack.show) showTable::Bool -> Char -> Char -> Char -> [[String]] -> String showTable _ _ _ _ [] = [] showTable header ver hor sep contents = unlines $ hr:(if header then z:hr:zs else intersperse hr zss) ++ [hr] where vss = map (map length) $ contents ms = map maximum $ transpose vss ::[Int] hr = concatMap (\ n -> sep : replicate n hor) ms ++ [sep] top = replicate (length hr) hor bss = map (\ps -> map (flip replicate ' ') $ zipWith (-) ms ps) $ vss zss@(z:zs) = zipWith (\us bs -> (concat $ zipWith (\x y -> (ver:x) ++ y) us bs) ++ [ver]) contents bss
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Generate an equivalent C++ version of this Haskell code.
import qualified Data.Text as T import Data.List main = do putStrLn $ showTable True ' ' '-' ' ' $ ["p","isPrime"]:map (\p -> [show p, show $ isPrime p]) numbers putStrLn $ "The first 120 prime numbers are:" putStrLn $ see 20 $ take 120 primes putStrLn "The 1,000th to 1,015th prime numbers are:" putStrLn $ see 16.take 16 $ drop 999 primes numbers = [2,3,9,15,29,37,47,57,67,77,87,97,237,409,659] primes = [p | p <- 2:[3,5..], isPrime p] isPrime :: Integer -> Bool isPrime p = if p < 2 then False else 0 == mod (succ $ product [1..pred p]) p bagOf :: Int -> [a] -> [[a]] bagOf _ [] = [] bagOf n xs = let (us,vs) = splitAt n xs in us : bagOf n vs see :: Show a => Int -> [a] -> String see n = unlines.map unwords.bagOf n.map (T.unpack.T.justifyRight 3 ' '.T.pack.show) showTable::Bool -> Char -> Char -> Char -> [[String]] -> String showTable _ _ _ _ [] = [] showTable header ver hor sep contents = unlines $ hr:(if header then z:hr:zs else intersperse hr zss) ++ [hr] where vss = map (map length) $ contents ms = map maximum $ transpose vss ::[Int] hr = concatMap (\ n -> sep : replicate n hor) ms ++ [sep] top = replicate (length hr) hor bss = map (\ps -> map (flip replicate ' ') $ zipWith (-) ms ps) $ vss zss@(z:zs) = zipWith (\us bs -> (concat $ zipWith (\x y -> (ver:x) ++ y) us bs) ++ [ver]) contents bss
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Preserve the algorithm and functionality while converting the code from Haskell to Java.
import qualified Data.Text as T import Data.List main = do putStrLn $ showTable True ' ' '-' ' ' $ ["p","isPrime"]:map (\p -> [show p, show $ isPrime p]) numbers putStrLn $ "The first 120 prime numbers are:" putStrLn $ see 20 $ take 120 primes putStrLn "The 1,000th to 1,015th prime numbers are:" putStrLn $ see 16.take 16 $ drop 999 primes numbers = [2,3,9,15,29,37,47,57,67,77,87,97,237,409,659] primes = [p | p <- 2:[3,5..], isPrime p] isPrime :: Integer -> Bool isPrime p = if p < 2 then False else 0 == mod (succ $ product [1..pred p]) p bagOf :: Int -> [a] -> [[a]] bagOf _ [] = [] bagOf n xs = let (us,vs) = splitAt n xs in us : bagOf n vs see :: Show a => Int -> [a] -> String see n = unlines.map unwords.bagOf n.map (T.unpack.T.justifyRight 3 ' '.T.pack.show) showTable::Bool -> Char -> Char -> Char -> [[String]] -> String showTable _ _ _ _ [] = [] showTable header ver hor sep contents = unlines $ hr:(if header then z:hr:zs else intersperse hr zss) ++ [hr] where vss = map (map length) $ contents ms = map maximum $ transpose vss ::[Int] hr = concatMap (\ n -> sep : replicate n hor) ms ++ [sep] top = replicate (length hr) hor bss = map (\ps -> map (flip replicate ' ') $ zipWith (-) ms ps) $ vss zss@(z:zs) = zipWith (\us bs -> (concat $ zipWith (\x y -> (ver:x) ++ y) us bs) ++ [ver]) contents bss
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Generate a Python translation of this Haskell snippet without changing its computational steps.
import qualified Data.Text as T import Data.List main = do putStrLn $ showTable True ' ' '-' ' ' $ ["p","isPrime"]:map (\p -> [show p, show $ isPrime p]) numbers putStrLn $ "The first 120 prime numbers are:" putStrLn $ see 20 $ take 120 primes putStrLn "The 1,000th to 1,015th prime numbers are:" putStrLn $ see 16.take 16 $ drop 999 primes numbers = [2,3,9,15,29,37,47,57,67,77,87,97,237,409,659] primes = [p | p <- 2:[3,5..], isPrime p] isPrime :: Integer -> Bool isPrime p = if p < 2 then False else 0 == mod (succ $ product [1..pred p]) p bagOf :: Int -> [a] -> [[a]] bagOf _ [] = [] bagOf n xs = let (us,vs) = splitAt n xs in us : bagOf n vs see :: Show a => Int -> [a] -> String see n = unlines.map unwords.bagOf n.map (T.unpack.T.justifyRight 3 ' '.T.pack.show) showTable::Bool -> Char -> Char -> Char -> [[String]] -> String showTable _ _ _ _ [] = [] showTable header ver hor sep contents = unlines $ hr:(if header then z:hr:zs else intersperse hr zss) ++ [hr] where vss = map (map length) $ contents ms = map maximum $ transpose vss ::[Int] hr = concatMap (\ n -> sep : replicate n hor) ms ++ [sep] top = replicate (length hr) hor bss = map (\ps -> map (flip replicate ' ') $ zipWith (-) ms ps) $ vss zss@(z:zs) = zipWith (\us bs -> (concat $ zipWith (\x y -> (ver:x) ++ y) us bs) ++ [ver]) contents bss
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Produce a functionally identical Go code for the snippet given in Haskell.
import qualified Data.Text as T import Data.List main = do putStrLn $ showTable True ' ' '-' ' ' $ ["p","isPrime"]:map (\p -> [show p, show $ isPrime p]) numbers putStrLn $ "The first 120 prime numbers are:" putStrLn $ see 20 $ take 120 primes putStrLn "The 1,000th to 1,015th prime numbers are:" putStrLn $ see 16.take 16 $ drop 999 primes numbers = [2,3,9,15,29,37,47,57,67,77,87,97,237,409,659] primes = [p | p <- 2:[3,5..], isPrime p] isPrime :: Integer -> Bool isPrime p = if p < 2 then False else 0 == mod (succ $ product [1..pred p]) p bagOf :: Int -> [a] -> [[a]] bagOf _ [] = [] bagOf n xs = let (us,vs) = splitAt n xs in us : bagOf n vs see :: Show a => Int -> [a] -> String see n = unlines.map unwords.bagOf n.map (T.unpack.T.justifyRight 3 ' '.T.pack.show) showTable::Bool -> Char -> Char -> Char -> [[String]] -> String showTable _ _ _ _ [] = [] showTable header ver hor sep contents = unlines $ hr:(if header then z:hr:zs else intersperse hr zss) ++ [hr] where vss = map (map length) $ contents ms = map maximum $ transpose vss ::[Int] hr = concatMap (\ n -> sep : replicate n hor) ms ++ [sep] top = replicate (length hr) hor bss = map (\ps -> map (flip replicate ' ') $ zipWith (-) ms ps) $ vss zss@(z:zs) = zipWith (\us bs -> (concat $ zipWith (\x y -> (ver:x) ++ y) us bs) ++ [ver]) contents bss
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Preserve the algorithm and functionality while converting the code from J to C.
wilson=: 0 = (| !&.:<:) (#~ wilson) x: 2 + i. 30 2 3 5 7 11 13 17 19 23 29 31
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Transform the following J implementation into C#, maintaining the same output and logic.
wilson=: 0 = (| !&.:<:) (#~ wilson) x: 2 + i. 30 2 3 5 7 11 13 17 19 23 29 31
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Generate a C++ translation of this J snippet without changing its computational steps.
wilson=: 0 = (| !&.:<:) (#~ wilson) x: 2 + i. 30 2 3 5 7 11 13 17 19 23 29 31
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Convert the following code from J to Java, ensuring the logic remains intact.
wilson=: 0 = (| !&.:<:) (#~ wilson) x: 2 + i. 30 2 3 5 7 11 13 17 19 23 29 31
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Translate this program into Python but keep the logic exactly as in J.
wilson=: 0 = (| !&.:<:) (#~ wilson) x: 2 + i. 30 2 3 5 7 11 13 17 19 23 29 31
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Generate a Go translation of this J snippet without changing its computational steps.
wilson=: 0 = (| !&.:<:) (#~ wilson) x: 2 + i. 30 2 3 5 7 11 13 17 19 23 29 31
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Preserve the algorithm and functionality while converting the code from Julia to C.
iswilsonprime(p) = (p < 2 || (p > 2 && iseven(p))) ? false : foldr((x, y) -> (x * y) % p, 1:p - 1) == p - 1 wilsonprimesbetween(n, m) = [i for i in n:m if iswilsonprime(i)] println("First 120 Wilson primes: ", wilsonprimesbetween(1, 1000)[1:120]) println("\nThe first 40 Wilson primes above 7900 are: ", wilsonprimesbetween(7900, 9000)[1:40])
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Write the same algorithm in C# as shown in this Julia implementation.
iswilsonprime(p) = (p < 2 || (p > 2 && iseven(p))) ? false : foldr((x, y) -> (x * y) % p, 1:p - 1) == p - 1 wilsonprimesbetween(n, m) = [i for i in n:m if iswilsonprime(i)] println("First 120 Wilson primes: ", wilsonprimesbetween(1, 1000)[1:120]) println("\nThe first 40 Wilson primes above 7900 are: ", wilsonprimesbetween(7900, 9000)[1:40])
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Please provide an equivalent version of this Julia code in C++.
iswilsonprime(p) = (p < 2 || (p > 2 && iseven(p))) ? false : foldr((x, y) -> (x * y) % p, 1:p - 1) == p - 1 wilsonprimesbetween(n, m) = [i for i in n:m if iswilsonprime(i)] println("First 120 Wilson primes: ", wilsonprimesbetween(1, 1000)[1:120]) println("\nThe first 40 Wilson primes above 7900 are: ", wilsonprimesbetween(7900, 9000)[1:40])
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Ensure the translated Java code behaves exactly like the original Julia snippet.
iswilsonprime(p) = (p < 2 || (p > 2 && iseven(p))) ? false : foldr((x, y) -> (x * y) % p, 1:p - 1) == p - 1 wilsonprimesbetween(n, m) = [i for i in n:m if iswilsonprime(i)] println("First 120 Wilson primes: ", wilsonprimesbetween(1, 1000)[1:120]) println("\nThe first 40 Wilson primes above 7900 are: ", wilsonprimesbetween(7900, 9000)[1:40])
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Can you help me rewrite this code in Python instead of Julia, keeping it the same logically?
iswilsonprime(p) = (p < 2 || (p > 2 && iseven(p))) ? false : foldr((x, y) -> (x * y) % p, 1:p - 1) == p - 1 wilsonprimesbetween(n, m) = [i for i in n:m if iswilsonprime(i)] println("First 120 Wilson primes: ", wilsonprimesbetween(1, 1000)[1:120]) println("\nThe first 40 Wilson primes above 7900 are: ", wilsonprimesbetween(7900, 9000)[1:40])
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Convert this Julia block to Go, preserving its control flow and logic.
iswilsonprime(p) = (p < 2 || (p > 2 && iseven(p))) ? false : foldr((x, y) -> (x * y) % p, 1:p - 1) == p - 1 wilsonprimesbetween(n, m) = [i for i in n:m if iswilsonprime(i)] println("First 120 Wilson primes: ", wilsonprimesbetween(1, 1000)[1:120]) println("\nThe first 40 Wilson primes above 7900 are: ", wilsonprimesbetween(7900, 9000)[1:40])
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Produce a language-to-language conversion: from Lua to C, same semantics.
function isWilsonPrime( n ) local fmodp = 1 for i = 2, n - 1 do fmodp = fmodp * i fmodp = fmodp % n end return fmodp == n - 1 end for n = -1, 100 do if isWilsonPrime( n ) then io.write( " " .. n ) end end
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Rewrite this program in C# while keeping its functionality equivalent to the Lua version.
function isWilsonPrime( n ) local fmodp = 1 for i = 2, n - 1 do fmodp = fmodp * i fmodp = fmodp % n end return fmodp == n - 1 end for n = -1, 100 do if isWilsonPrime( n ) then io.write( " " .. n ) end end
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Port the provided Lua code into C++ while preserving the original functionality.
function isWilsonPrime( n ) local fmodp = 1 for i = 2, n - 1 do fmodp = fmodp * i fmodp = fmodp % n end return fmodp == n - 1 end for n = -1, 100 do if isWilsonPrime( n ) then io.write( " " .. n ) end end
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Write a version of this Lua function in Java with identical behavior.
function isWilsonPrime( n ) local fmodp = 1 for i = 2, n - 1 do fmodp = fmodp * i fmodp = fmodp % n end return fmodp == n - 1 end for n = -1, 100 do if isWilsonPrime( n ) then io.write( " " .. n ) end end
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Maintain the same structure and functionality when rewriting this code in Python.
function isWilsonPrime( n ) local fmodp = 1 for i = 2, n - 1 do fmodp = fmodp * i fmodp = fmodp % n end return fmodp == n - 1 end for n = -1, 100 do if isWilsonPrime( n ) then io.write( " " .. n ) end end
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Write the same code in Go as shown below in Lua.
function isWilsonPrime( n ) local fmodp = 1 for i = 2, n - 1 do fmodp = fmodp * i fmodp = fmodp % n end return fmodp == n - 1 end for n = -1, 100 do if isWilsonPrime( n ) then io.write( " " .. n ) end end
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Can you help me rewrite this code in C instead of Mathematica, keeping it the same logically?
ClearAll[WilsonPrimeQ] WilsonPrimeQ[1] = False; WilsonPrimeQ[p_Integer] := Divisible[(p - 1)! + 1, p] Select[Range[100], WilsonPrimeQ]
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Write the same algorithm in C# as shown in this Mathematica implementation.
ClearAll[WilsonPrimeQ] WilsonPrimeQ[1] = False; WilsonPrimeQ[p_Integer] := Divisible[(p - 1)! + 1, p] Select[Range[100], WilsonPrimeQ]
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Rewrite this program in C++ while keeping its functionality equivalent to the Mathematica version.
ClearAll[WilsonPrimeQ] WilsonPrimeQ[1] = False; WilsonPrimeQ[p_Integer] := Divisible[(p - 1)! + 1, p] Select[Range[100], WilsonPrimeQ]
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Convert this Mathematica block to Java, preserving its control flow and logic.
ClearAll[WilsonPrimeQ] WilsonPrimeQ[1] = False; WilsonPrimeQ[p_Integer] := Divisible[(p - 1)! + 1, p] Select[Range[100], WilsonPrimeQ]
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Port the provided Mathematica code into Python while preserving the original functionality.
ClearAll[WilsonPrimeQ] WilsonPrimeQ[1] = False; WilsonPrimeQ[p_Integer] := Divisible[(p - 1)! + 1, p] Select[Range[100], WilsonPrimeQ]
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Convert the following code from Mathematica to Go, ensuring the logic remains intact.
ClearAll[WilsonPrimeQ] WilsonPrimeQ[1] = False; WilsonPrimeQ[p_Integer] := Divisible[(p - 1)! + 1, p] Select[Range[100], WilsonPrimeQ]
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Write the same code in C as shown below in Nim.
import strutils, sugar proc facmod(n, m: int): int = result = 1 for k in 2..n: result = (result * k) mod m func isPrime(n: int): bool = (facmod(n - 1, n) + 1) mod n == 0 let primes = collect(newSeq): for n in 2..100: if n.isPrime: n echo "Prime numbers between 2 and 100:" echo primes.join(" ")
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Write the same code in C# as shown below in Nim.
import strutils, sugar proc facmod(n, m: int): int = result = 1 for k in 2..n: result = (result * k) mod m func isPrime(n: int): bool = (facmod(n - 1, n) + 1) mod n == 0 let primes = collect(newSeq): for n in 2..100: if n.isPrime: n echo "Prime numbers between 2 and 100:" echo primes.join(" ")
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Rewrite this program in C++ while keeping its functionality equivalent to the Nim version.
import strutils, sugar proc facmod(n, m: int): int = result = 1 for k in 2..n: result = (result * k) mod m func isPrime(n: int): bool = (facmod(n - 1, n) + 1) mod n == 0 let primes = collect(newSeq): for n in 2..100: if n.isPrime: n echo "Prime numbers between 2 and 100:" echo primes.join(" ")
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Produce a functionally identical Java code for the snippet given in Nim.
import strutils, sugar proc facmod(n, m: int): int = result = 1 for k in 2..n: result = (result * k) mod m func isPrime(n: int): bool = (facmod(n - 1, n) + 1) mod n == 0 let primes = collect(newSeq): for n in 2..100: if n.isPrime: n echo "Prime numbers between 2 and 100:" echo primes.join(" ")
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Transform the following Nim implementation into Python, maintaining the same output and logic.
import strutils, sugar proc facmod(n, m: int): int = result = 1 for k in 2..n: result = (result * k) mod m func isPrime(n: int): bool = (facmod(n - 1, n) + 1) mod n == 0 let primes = collect(newSeq): for n in 2..100: if n.isPrime: n echo "Prime numbers between 2 and 100:" echo primes.join(" ")
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Port the following code from Nim to Go with equivalent syntax and logic.
import strutils, sugar proc facmod(n, m: int): int = result = 1 for k in 2..n: result = (result * k) mod m func isPrime(n: int): bool = (facmod(n - 1, n) + 1) mod n == 0 let primes = collect(newSeq): for n in 2..100: if n.isPrime: n echo "Prime numbers between 2 and 100:" echo primes.join(" ")
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Convert this Pascal snippet to C and keep its semantics consistent.
program PrimesByWilson; uses SysUtils; function WilsonFullCalc( n : longword) : boolean; var f, m : longword; begin if n < 2 then begin result := false; exit; end; f := 1; for m := 2 to n - 1 do begin f := (uint64(f) * uint64(m)) mod n; end; result := (f = n - 1); end; function WilsonShortCut( n : longword) : boolean; var f, g, h, m, m2inc, r : longword; begin if n < 2 then begin result := false; exit; end; f := 1; m := 1; m2inc := 3; r := n - 1; while r >= m2inc do begin inc(m); f := (uint64(f) * uint64(m)) mod n; dec( r, m2inc); inc( m2inc, 2); end; h := n; while f <> 0 do begin g := h mod f; h := f; f := g; end; result := (h = 1); end; type TPrimalityTest = function( n : longword) : boolean; procedure ShowPrimes( isPrime : TPrimalityTest; minValue, maxValue : longword); var n : longword; begin WriteLn( 'Primes in ', minValue, '..', maxValue); for n := minValue to maxValue do if isPrime(n) then Write(' ', n); WriteLn; end; begin WriteLn( 'By full calculation:'); ShowPrimes( @WilsonFullCalc, 1, 100); ShowPrimes( @WilsonFullCalc, 1000, 1100); WriteLn; WriteLn( 'Using the short cut:'); ShowPrimes( @WilsonShortCut, 1, 100); ShowPrimes( @WilsonShortCut, 1000, 1100); ShowPrimes( @WilsonShortCut, 4294967195, 4294967295 ); end.
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Generate a C# translation of this Pascal snippet without changing its computational steps.
program PrimesByWilson; uses SysUtils; function WilsonFullCalc( n : longword) : boolean; var f, m : longword; begin if n < 2 then begin result := false; exit; end; f := 1; for m := 2 to n - 1 do begin f := (uint64(f) * uint64(m)) mod n; end; result := (f = n - 1); end; function WilsonShortCut( n : longword) : boolean; var f, g, h, m, m2inc, r : longword; begin if n < 2 then begin result := false; exit; end; f := 1; m := 1; m2inc := 3; r := n - 1; while r >= m2inc do begin inc(m); f := (uint64(f) * uint64(m)) mod n; dec( r, m2inc); inc( m2inc, 2); end; h := n; while f <> 0 do begin g := h mod f; h := f; f := g; end; result := (h = 1); end; type TPrimalityTest = function( n : longword) : boolean; procedure ShowPrimes( isPrime : TPrimalityTest; minValue, maxValue : longword); var n : longword; begin WriteLn( 'Primes in ', minValue, '..', maxValue); for n := minValue to maxValue do if isPrime(n) then Write(' ', n); WriteLn; end; begin WriteLn( 'By full calculation:'); ShowPrimes( @WilsonFullCalc, 1, 100); ShowPrimes( @WilsonFullCalc, 1000, 1100); WriteLn; WriteLn( 'Using the short cut:'); ShowPrimes( @WilsonShortCut, 1, 100); ShowPrimes( @WilsonShortCut, 1000, 1100); ShowPrimes( @WilsonShortCut, 4294967195, 4294967295 ); end.
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Rewrite this program in C++ while keeping its functionality equivalent to the Pascal version.
program PrimesByWilson; uses SysUtils; function WilsonFullCalc( n : longword) : boolean; var f, m : longword; begin if n < 2 then begin result := false; exit; end; f := 1; for m := 2 to n - 1 do begin f := (uint64(f) * uint64(m)) mod n; end; result := (f = n - 1); end; function WilsonShortCut( n : longword) : boolean; var f, g, h, m, m2inc, r : longword; begin if n < 2 then begin result := false; exit; end; f := 1; m := 1; m2inc := 3; r := n - 1; while r >= m2inc do begin inc(m); f := (uint64(f) * uint64(m)) mod n; dec( r, m2inc); inc( m2inc, 2); end; h := n; while f <> 0 do begin g := h mod f; h := f; f := g; end; result := (h = 1); end; type TPrimalityTest = function( n : longword) : boolean; procedure ShowPrimes( isPrime : TPrimalityTest; minValue, maxValue : longword); var n : longword; begin WriteLn( 'Primes in ', minValue, '..', maxValue); for n := minValue to maxValue do if isPrime(n) then Write(' ', n); WriteLn; end; begin WriteLn( 'By full calculation:'); ShowPrimes( @WilsonFullCalc, 1, 100); ShowPrimes( @WilsonFullCalc, 1000, 1100); WriteLn; WriteLn( 'Using the short cut:'); ShowPrimes( @WilsonShortCut, 1, 100); ShowPrimes( @WilsonShortCut, 1000, 1100); ShowPrimes( @WilsonShortCut, 4294967195, 4294967295 ); end.
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Convert this Pascal snippet to Java and keep its semantics consistent.
program PrimesByWilson; uses SysUtils; function WilsonFullCalc( n : longword) : boolean; var f, m : longword; begin if n < 2 then begin result := false; exit; end; f := 1; for m := 2 to n - 1 do begin f := (uint64(f) * uint64(m)) mod n; end; result := (f = n - 1); end; function WilsonShortCut( n : longword) : boolean; var f, g, h, m, m2inc, r : longword; begin if n < 2 then begin result := false; exit; end; f := 1; m := 1; m2inc := 3; r := n - 1; while r >= m2inc do begin inc(m); f := (uint64(f) * uint64(m)) mod n; dec( r, m2inc); inc( m2inc, 2); end; h := n; while f <> 0 do begin g := h mod f; h := f; f := g; end; result := (h = 1); end; type TPrimalityTest = function( n : longword) : boolean; procedure ShowPrimes( isPrime : TPrimalityTest; minValue, maxValue : longword); var n : longword; begin WriteLn( 'Primes in ', minValue, '..', maxValue); for n := minValue to maxValue do if isPrime(n) then Write(' ', n); WriteLn; end; begin WriteLn( 'By full calculation:'); ShowPrimes( @WilsonFullCalc, 1, 100); ShowPrimes( @WilsonFullCalc, 1000, 1100); WriteLn; WriteLn( 'Using the short cut:'); ShowPrimes( @WilsonShortCut, 1, 100); ShowPrimes( @WilsonShortCut, 1000, 1100); ShowPrimes( @WilsonShortCut, 4294967195, 4294967295 ); end.
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Change the programming language of this snippet from Pascal to Python without modifying what it does.
program PrimesByWilson; uses SysUtils; function WilsonFullCalc( n : longword) : boolean; var f, m : longword; begin if n < 2 then begin result := false; exit; end; f := 1; for m := 2 to n - 1 do begin f := (uint64(f) * uint64(m)) mod n; end; result := (f = n - 1); end; function WilsonShortCut( n : longword) : boolean; var f, g, h, m, m2inc, r : longword; begin if n < 2 then begin result := false; exit; end; f := 1; m := 1; m2inc := 3; r := n - 1; while r >= m2inc do begin inc(m); f := (uint64(f) * uint64(m)) mod n; dec( r, m2inc); inc( m2inc, 2); end; h := n; while f <> 0 do begin g := h mod f; h := f; f := g; end; result := (h = 1); end; type TPrimalityTest = function( n : longword) : boolean; procedure ShowPrimes( isPrime : TPrimalityTest; minValue, maxValue : longword); var n : longword; begin WriteLn( 'Primes in ', minValue, '..', maxValue); for n := minValue to maxValue do if isPrime(n) then Write(' ', n); WriteLn; end; begin WriteLn( 'By full calculation:'); ShowPrimes( @WilsonFullCalc, 1, 100); ShowPrimes( @WilsonFullCalc, 1000, 1100); WriteLn; WriteLn( 'Using the short cut:'); ShowPrimes( @WilsonShortCut, 1, 100); ShowPrimes( @WilsonShortCut, 1000, 1100); ShowPrimes( @WilsonShortCut, 4294967195, 4294967295 ); end.
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Convert this Pascal block to Go, preserving its control flow and logic.
program PrimesByWilson; uses SysUtils; function WilsonFullCalc( n : longword) : boolean; var f, m : longword; begin if n < 2 then begin result := false; exit; end; f := 1; for m := 2 to n - 1 do begin f := (uint64(f) * uint64(m)) mod n; end; result := (f = n - 1); end; function WilsonShortCut( n : longword) : boolean; var f, g, h, m, m2inc, r : longword; begin if n < 2 then begin result := false; exit; end; f := 1; m := 1; m2inc := 3; r := n - 1; while r >= m2inc do begin inc(m); f := (uint64(f) * uint64(m)) mod n; dec( r, m2inc); inc( m2inc, 2); end; h := n; while f <> 0 do begin g := h mod f; h := f; f := g; end; result := (h = 1); end; type TPrimalityTest = function( n : longword) : boolean; procedure ShowPrimes( isPrime : TPrimalityTest; minValue, maxValue : longword); var n : longword; begin WriteLn( 'Primes in ', minValue, '..', maxValue); for n := minValue to maxValue do if isPrime(n) then Write(' ', n); WriteLn; end; begin WriteLn( 'By full calculation:'); ShowPrimes( @WilsonFullCalc, 1, 100); ShowPrimes( @WilsonFullCalc, 1000, 1100); WriteLn; WriteLn( 'Using the short cut:'); ShowPrimes( @WilsonShortCut, 1, 100); ShowPrimes( @WilsonShortCut, 1000, 1100); ShowPrimes( @WilsonShortCut, 4294967195, 4294967295 ); end.
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Ensure the translated C code behaves exactly like the original Perl snippet.
use strict; use warnings; use feature 'say'; use ntheory qw(factorial); my($ends_in_7, $ends_in_3); sub is_wilson_prime { my($n) = @_; $n > 1 or return 0; (factorial($n-1) % $n) == ($n-1) ? 1 : 0; } for (0..50) { my $m = 3 + 10 * $_; $ends_in_3 .= "$m " if is_wilson_prime($m); my $n = 7 + 10 * $_; $ends_in_7 .= "$n " if is_wilson_prime($n); } say $ends_in_3; say $ends_in_7;
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Preserve the algorithm and functionality while converting the code from Perl to C#.
use strict; use warnings; use feature 'say'; use ntheory qw(factorial); my($ends_in_7, $ends_in_3); sub is_wilson_prime { my($n) = @_; $n > 1 or return 0; (factorial($n-1) % $n) == ($n-1) ? 1 : 0; } for (0..50) { my $m = 3 + 10 * $_; $ends_in_3 .= "$m " if is_wilson_prime($m); my $n = 7 + 10 * $_; $ends_in_7 .= "$n " if is_wilson_prime($n); } say $ends_in_3; say $ends_in_7;
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Translate this program into C++ but keep the logic exactly as in Perl.
use strict; use warnings; use feature 'say'; use ntheory qw(factorial); my($ends_in_7, $ends_in_3); sub is_wilson_prime { my($n) = @_; $n > 1 or return 0; (factorial($n-1) % $n) == ($n-1) ? 1 : 0; } for (0..50) { my $m = 3 + 10 * $_; $ends_in_3 .= "$m " if is_wilson_prime($m); my $n = 7 + 10 * $_; $ends_in_7 .= "$n " if is_wilson_prime($n); } say $ends_in_3; say $ends_in_7;
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Produce a functionally identical Java code for the snippet given in Perl.
use strict; use warnings; use feature 'say'; use ntheory qw(factorial); my($ends_in_7, $ends_in_3); sub is_wilson_prime { my($n) = @_; $n > 1 or return 0; (factorial($n-1) % $n) == ($n-1) ? 1 : 0; } for (0..50) { my $m = 3 + 10 * $_; $ends_in_3 .= "$m " if is_wilson_prime($m); my $n = 7 + 10 * $_; $ends_in_7 .= "$n " if is_wilson_prime($n); } say $ends_in_3; say $ends_in_7;
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Write the same algorithm in Python as shown in this Perl implementation.
use strict; use warnings; use feature 'say'; use ntheory qw(factorial); my($ends_in_7, $ends_in_3); sub is_wilson_prime { my($n) = @_; $n > 1 or return 0; (factorial($n-1) % $n) == ($n-1) ? 1 : 0; } for (0..50) { my $m = 3 + 10 * $_; $ends_in_3 .= "$m " if is_wilson_prime($m); my $n = 7 + 10 * $_; $ends_in_7 .= "$n " if is_wilson_prime($n); } say $ends_in_3; say $ends_in_7;
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Generate a Go translation of this Perl snippet without changing its computational steps.
use strict; use warnings; use feature 'say'; use ntheory qw(factorial); my($ends_in_7, $ends_in_3); sub is_wilson_prime { my($n) = @_; $n > 1 or return 0; (factorial($n-1) % $n) == ($n-1) ? 1 : 0; } for (0..50) { my $m = 3 + 10 * $_; $ends_in_3 .= "$m " if is_wilson_prime($m); my $n = 7 + 10 * $_; $ends_in_7 .= "$n " if is_wilson_prime($n); } say $ends_in_3; say $ends_in_7;
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Translate this program into C but keep the logic exactly as in REXX.
parse arg LO zz if LO=='' | LO=="," then LO= 120 if zz ='' | zz ="," then zz=2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 sw= linesize() - 1; if sw<1 then sw= 79 digs = digits() #= 0 !.= 1 $= do p=1 until #=LO; oDigs= digs ?= isPrimeW(p) if digs>Odigs then numeric digits digs if \? then iterate #= # + 1; $= $ p end call show 'The first ' LO " prime numbers are:" w= max( length(LO), length(word(reverse(zz),1))) @is.0= " isn't"; @is.1= 'is' say do z=1 for words(zz); oDigs= digs p= word(zz, z) ?= isPrimeW(p) if digs>Odigs then numeric digits digs say right(p, max(w,length(p) ) ) @is.? "prime." end exit isPrimeW: procedure expose !. digs; parse arg x '' -1 last; != 1; xm= x - 1 if x<2 then return 0 if x==2 | x==5 then return 1 if last//2==0 | last==5 then return 0 if !.xm\==1 then != !.xm else do; if xm>!.0 then do; base= !.0+1; _= !.0; != !._; end else base= 2 do j=!.0+1 to xm; != ! * j if pos(., !)\==0 then do; parse var ! 'E' expon numeric digits expon +99 digs = digits() end end if xm<999 then do; !.xm=!; !.0=xm; end end if (!+1)//x==0 then return 1 return 0 show: parse arg header,oo; say header w= length( word($, LO) ) do k=1 for LO; _= right( word($, k), w) if length(oo _)>sw then do; say substr(oo,2); oo=; end oo= oo _ end if oo\='' then say substr(oo, 2); return
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Convert the following code from REXX to C#, ensuring the logic remains intact.
parse arg LO zz if LO=='' | LO=="," then LO= 120 if zz ='' | zz ="," then zz=2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 sw= linesize() - 1; if sw<1 then sw= 79 digs = digits() #= 0 !.= 1 $= do p=1 until #=LO; oDigs= digs ?= isPrimeW(p) if digs>Odigs then numeric digits digs if \? then iterate #= # + 1; $= $ p end call show 'The first ' LO " prime numbers are:" w= max( length(LO), length(word(reverse(zz),1))) @is.0= " isn't"; @is.1= 'is' say do z=1 for words(zz); oDigs= digs p= word(zz, z) ?= isPrimeW(p) if digs>Odigs then numeric digits digs say right(p, max(w,length(p) ) ) @is.? "prime." end exit isPrimeW: procedure expose !. digs; parse arg x '' -1 last; != 1; xm= x - 1 if x<2 then return 0 if x==2 | x==5 then return 1 if last//2==0 | last==5 then return 0 if !.xm\==1 then != !.xm else do; if xm>!.0 then do; base= !.0+1; _= !.0; != !._; end else base= 2 do j=!.0+1 to xm; != ! * j if pos(., !)\==0 then do; parse var ! 'E' expon numeric digits expon +99 digs = digits() end end if xm<999 then do; !.xm=!; !.0=xm; end end if (!+1)//x==0 then return 1 return 0 show: parse arg header,oo; say header w= length( word($, LO) ) do k=1 for LO; _= right( word($, k), w) if length(oo _)>sw then do; say substr(oo,2); oo=; end oo= oo _ end if oo\='' then say substr(oo, 2); return
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Preserve the algorithm and functionality while converting the code from REXX to C++.
parse arg LO zz if LO=='' | LO=="," then LO= 120 if zz ='' | zz ="," then zz=2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 sw= linesize() - 1; if sw<1 then sw= 79 digs = digits() #= 0 !.= 1 $= do p=1 until #=LO; oDigs= digs ?= isPrimeW(p) if digs>Odigs then numeric digits digs if \? then iterate #= # + 1; $= $ p end call show 'The first ' LO " prime numbers are:" w= max( length(LO), length(word(reverse(zz),1))) @is.0= " isn't"; @is.1= 'is' say do z=1 for words(zz); oDigs= digs p= word(zz, z) ?= isPrimeW(p) if digs>Odigs then numeric digits digs say right(p, max(w,length(p) ) ) @is.? "prime." end exit isPrimeW: procedure expose !. digs; parse arg x '' -1 last; != 1; xm= x - 1 if x<2 then return 0 if x==2 | x==5 then return 1 if last//2==0 | last==5 then return 0 if !.xm\==1 then != !.xm else do; if xm>!.0 then do; base= !.0+1; _= !.0; != !._; end else base= 2 do j=!.0+1 to xm; != ! * j if pos(., !)\==0 then do; parse var ! 'E' expon numeric digits expon +99 digs = digits() end end if xm<999 then do; !.xm=!; !.0=xm; end end if (!+1)//x==0 then return 1 return 0 show: parse arg header,oo; say header w= length( word($, LO) ) do k=1 for LO; _= right( word($, k), w) if length(oo _)>sw then do; say substr(oo,2); oo=; end oo= oo _ end if oo\='' then say substr(oo, 2); return
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Change the following REXX code into Java without altering its purpose.
parse arg LO zz if LO=='' | LO=="," then LO= 120 if zz ='' | zz ="," then zz=2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 sw= linesize() - 1; if sw<1 then sw= 79 digs = digits() #= 0 !.= 1 $= do p=1 until #=LO; oDigs= digs ?= isPrimeW(p) if digs>Odigs then numeric digits digs if \? then iterate #= # + 1; $= $ p end call show 'The first ' LO " prime numbers are:" w= max( length(LO), length(word(reverse(zz),1))) @is.0= " isn't"; @is.1= 'is' say do z=1 for words(zz); oDigs= digs p= word(zz, z) ?= isPrimeW(p) if digs>Odigs then numeric digits digs say right(p, max(w,length(p) ) ) @is.? "prime." end exit isPrimeW: procedure expose !. digs; parse arg x '' -1 last; != 1; xm= x - 1 if x<2 then return 0 if x==2 | x==5 then return 1 if last//2==0 | last==5 then return 0 if !.xm\==1 then != !.xm else do; if xm>!.0 then do; base= !.0+1; _= !.0; != !._; end else base= 2 do j=!.0+1 to xm; != ! * j if pos(., !)\==0 then do; parse var ! 'E' expon numeric digits expon +99 digs = digits() end end if xm<999 then do; !.xm=!; !.0=xm; end end if (!+1)//x==0 then return 1 return 0 show: parse arg header,oo; say header w= length( word($, LO) ) do k=1 for LO; _= right( word($, k), w) if length(oo _)>sw then do; say substr(oo,2); oo=; end oo= oo _ end if oo\='' then say substr(oo, 2); return
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Generate an equivalent Python version of this REXX code.
parse arg LO zz if LO=='' | LO=="," then LO= 120 if zz ='' | zz ="," then zz=2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 sw= linesize() - 1; if sw<1 then sw= 79 digs = digits() #= 0 !.= 1 $= do p=1 until #=LO; oDigs= digs ?= isPrimeW(p) if digs>Odigs then numeric digits digs if \? then iterate #= # + 1; $= $ p end call show 'The first ' LO " prime numbers are:" w= max( length(LO), length(word(reverse(zz),1))) @is.0= " isn't"; @is.1= 'is' say do z=1 for words(zz); oDigs= digs p= word(zz, z) ?= isPrimeW(p) if digs>Odigs then numeric digits digs say right(p, max(w,length(p) ) ) @is.? "prime." end exit isPrimeW: procedure expose !. digs; parse arg x '' -1 last; != 1; xm= x - 1 if x<2 then return 0 if x==2 | x==5 then return 1 if last//2==0 | last==5 then return 0 if !.xm\==1 then != !.xm else do; if xm>!.0 then do; base= !.0+1; _= !.0; != !._; end else base= 2 do j=!.0+1 to xm; != ! * j if pos(., !)\==0 then do; parse var ! 'E' expon numeric digits expon +99 digs = digits() end end if xm<999 then do; !.xm=!; !.0=xm; end end if (!+1)//x==0 then return 1 return 0 show: parse arg header,oo; say header w= length( word($, LO) ) do k=1 for LO; _= right( word($, k), w) if length(oo _)>sw then do; say substr(oo,2); oo=; end oo= oo _ end if oo\='' then say substr(oo, 2); return
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Convert this REXX block to Go, preserving its control flow and logic.
parse arg LO zz if LO=='' | LO=="," then LO= 120 if zz ='' | zz ="," then zz=2 3 9 15 29 37 47 57 67 77 87 97 237 409 659 sw= linesize() - 1; if sw<1 then sw= 79 digs = digits() #= 0 !.= 1 $= do p=1 until #=LO; oDigs= digs ?= isPrimeW(p) if digs>Odigs then numeric digits digs if \? then iterate #= # + 1; $= $ p end call show 'The first ' LO " prime numbers are:" w= max( length(LO), length(word(reverse(zz),1))) @is.0= " isn't"; @is.1= 'is' say do z=1 for words(zz); oDigs= digs p= word(zz, z) ?= isPrimeW(p) if digs>Odigs then numeric digits digs say right(p, max(w,length(p) ) ) @is.? "prime." end exit isPrimeW: procedure expose !. digs; parse arg x '' -1 last; != 1; xm= x - 1 if x<2 then return 0 if x==2 | x==5 then return 1 if last//2==0 | last==5 then return 0 if !.xm\==1 then != !.xm else do; if xm>!.0 then do; base= !.0+1; _= !.0; != !._; end else base= 2 do j=!.0+1 to xm; != ! * j if pos(., !)\==0 then do; parse var ! 'E' expon numeric digits expon +99 digs = digits() end end if xm<999 then do; !.xm=!; !.0=xm; end end if (!+1)//x==0 then return 1 return 0 show: parse arg header,oo; say header w= length( word($, LO) ) do k=1 for LO; _= right( word($, k), w) if length(oo _)>sw then do; say substr(oo,2); oo=; end oo= oo _ end if oo\='' then say substr(oo, 2); return
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Produce a functionally identical C code for the snippet given in Ruby.
def w_prime?(i) return false if i < 2 ((1..i-1).inject(&:*) + 1) % i == 0 end p (1..100).select{|n| w_prime?(n) }
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Convert this Ruby block to C#, preserving its control flow and logic.
def w_prime?(i) return false if i < 2 ((1..i-1).inject(&:*) + 1) % i == 0 end p (1..100).select{|n| w_prime?(n) }
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Rewrite this program in C++ while keeping its functionality equivalent to the Ruby version.
def w_prime?(i) return false if i < 2 ((1..i-1).inject(&:*) + 1) % i == 0 end p (1..100).select{|n| w_prime?(n) }
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Write the same code in Java as shown below in Ruby.
def w_prime?(i) return false if i < 2 ((1..i-1).inject(&:*) + 1) % i == 0 end p (1..100).select{|n| w_prime?(n) }
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Rewrite this program in Python while keeping its functionality equivalent to the Ruby version.
def w_prime?(i) return false if i < 2 ((1..i-1).inject(&:*) + 1) % i == 0 end p (1..100).select{|n| w_prime?(n) }
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Preserve the algorithm and functionality while converting the code from Ruby to Go.
def w_prime?(i) return false if i < 2 ((1..i-1).inject(&:*) + 1) % i == 0 end p (1..100).select{|n| w_prime?(n) }
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Produce a functionally identical C code for the snippet given in Swift.
import BigInt func factorial<T: BinaryInteger>(_ n: T) -> T { guard n != 0 else { return 1 } return stride(from: n, to: 0, by: -1).reduce(1, *) } func isWilsonPrime<T: BinaryInteger>(_ n: T) -> Bool { guard n >= 2 else { return false } return (factorial(n - 1) + 1) % n == 0 } print((1...100).map({ BigInt($0) }).filter(isWilsonPrime))
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
Write the same algorithm in C# as shown in this Swift implementation.
import BigInt func factorial<T: BinaryInteger>(_ n: T) -> T { guard n != 0 else { return 1 } return stride(from: n, to: 0, by: -1).reduce(1, *) } func isWilsonPrime<T: BinaryInteger>(_ n: T) -> Bool { guard n >= 2 else { return false } return (factorial(n - 1) + 1) % n == 0 } print((1...100).map({ BigInt($0) }).filter(isWilsonPrime))
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
Keep all operations the same but rewrite the snippet in C++.
import BigInt func factorial<T: BinaryInteger>(_ n: T) -> T { guard n != 0 else { return 1 } return stride(from: n, to: 0, by: -1).reduce(1, *) } func isWilsonPrime<T: BinaryInteger>(_ n: T) -> Bool { guard n >= 2 else { return false } return (factorial(n - 1) + 1) % n == 0 } print((1...100).map({ BigInt($0) }).filter(isWilsonPrime))
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
Generate an equivalent Java version of this Swift code.
import BigInt func factorial<T: BinaryInteger>(_ n: T) -> T { guard n != 0 else { return 1 } return stride(from: n, to: 0, by: -1).reduce(1, *) } func isWilsonPrime<T: BinaryInteger>(_ n: T) -> Bool { guard n >= 2 else { return false } return (factorial(n - 1) + 1) % n == 0 } print((1...100).map({ BigInt($0) }).filter(isWilsonPrime))
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
Maintain the same structure and functionality when rewriting this code in Python.
import BigInt func factorial<T: BinaryInteger>(_ n: T) -> T { guard n != 0 else { return 1 } return stride(from: n, to: 0, by: -1).reduce(1, *) } func isWilsonPrime<T: BinaryInteger>(_ n: T) -> Bool { guard n >= 2 else { return false } return (factorial(n - 1) + 1) % n == 0 } print((1...100).map({ BigInt($0) }).filter(isWilsonPrime))
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Transform the following Swift implementation into Go, maintaining the same output and logic.
import BigInt func factorial<T: BinaryInteger>(_ n: T) -> T { guard n != 0 else { return 1 } return stride(from: n, to: 0, by: -1).reduce(1, *) } func isWilsonPrime<T: BinaryInteger>(_ n: T) -> Bool { guard n >= 2 else { return false } return (factorial(n - 1) + 1) % n == 0 } print((1...100).map({ BigInt($0) }).filter(isWilsonPrime))
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
Produce a functionally identical Rust code for the snippet given in C.
#include <stdbool.h> #include <stdint.h> #include <stdio.h> uint64_t factorial(uint64_t n) { uint64_t product = 1; if (n < 2) { return 1; } for (; n > 0; n--) { uint64_t prev = product; product *= n; if (product < prev) { fprintf(stderr, "Overflowed\n"); return product; } } return product; } bool isPrime(uint64_t n) { uint64_t large = factorial(n - 1) + 1; return (large % n) == 0; } int main() { uint64_t n; for (n = 2; n < 22; n++) { printf("Is %llu prime: %d\n", n, isPrime(n)); } return 0; }
fn factorial_mod(mut n: u32, p: u32) -> u32 { let mut f = 1; while n != 0 && f != 0 { f = (f * n) % p; n -= 1; } f } fn is_prime(p: u32) -> bool { p > 1 && factorial_mod(p - 1, p) == p - 1 } fn main() { println!(" n | prime?\n------------"); for p in vec![2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659] { println!("{:>3} | {}", p, is_prime(p)); } println!("\nFirst 120 primes by Wilson's theorem:"); let mut n = 0; let mut p = 1; while n < 120 { if is_prime(p) { n += 1; print!("{:>3}{}", p, if n % 20 == 0 { '\n' } else { ' ' }); } p += 1; } println!("\n1000th through 1015th primes:"); let mut i = 0; while n < 1015 { if is_prime(p) { n += 1; if n >= 1000 { i += 1; print!("{:>3}{}", p, if i % 16 == 0 { '\n' } else { ' ' }); } } p += 1; } }
Change the programming language of this snippet from C++ to Rust without modifying what it does.
#include <iomanip> #include <iostream> int factorial_mod(int n, int p) { int f = 1; for (; n > 0 && f != 0; --n) f = (f * n) % p; return f; } bool is_prime(int p) { return p > 1 && factorial_mod(p - 1, p) == p - 1; } int main() { std::cout << " n | prime?\n------------\n"; std::cout << std::boolalpha; for (int p : {2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659}) std::cout << std::setw(3) << p << " | " << is_prime(p) << '\n'; std::cout << "\nFirst 120 primes by Wilson's theorem:\n"; int n = 0, p = 1; for (; n < 120; ++p) { if (is_prime(p)) std::cout << std::setw(3) << p << (++n % 20 == 0 ? '\n' : ' '); } std::cout << "\n1000th through 1015th primes:\n"; for (int i = 0; n < 1015; ++p) { if (is_prime(p)) { if (++n >= 1000) std::cout << std::setw(4) << p << (++i % 16 == 0 ? '\n' : ' '); } } }
fn factorial_mod(mut n: u32, p: u32) -> u32 { let mut f = 1; while n != 0 && f != 0 { f = (f * n) % p; n -= 1; } f } fn is_prime(p: u32) -> bool { p > 1 && factorial_mod(p - 1, p) == p - 1 } fn main() { println!(" n | prime?\n------------"); for p in vec![2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659] { println!("{:>3} | {}", p, is_prime(p)); } println!("\nFirst 120 primes by Wilson's theorem:"); let mut n = 0; let mut p = 1; while n < 120 { if is_prime(p) { n += 1; print!("{:>3}{}", p, if n % 20 == 0 { '\n' } else { ' ' }); } p += 1; } println!("\n1000th through 1015th primes:"); let mut i = 0; while n < 1015 { if is_prime(p) { n += 1; if n >= 1000 { i += 1; print!("{:>3}{}", p, if i % 16 == 0 { '\n' } else { ' ' }); } } p += 1; } }
Write the same algorithm in Rust as shown in this C# implementation.
using System; using System.Linq; using System.Collections; using static System.Console; using System.Collections.Generic; using BI = System.Numerics.BigInteger; class Program { const int fst = 120, skp = 1000, max = 1015; static double et1, et2; static DateTime st; static string ms1 = "Wilson's theorem method", ms2 = "Sieve of Eratosthenes method", fmt = "--- {0} ---\n\nThe first {1} primes are:", fm2 = "{0} prime thru the {1} prime:"; static List<int> lst = new List<int>(); static void Dump(int s, int t, string f) { foreach (var item in lst.Skip(s).Take(t)) Write(f, item); WriteLine("\n"); } static string Ord(int x, string fmt = "{0:n0}") { var y = x % 10; if ((x % 100) / 10 == 10 || y > 3) y = 0; return string.Format(fmt, x) + "thstndrd".Substring(y << 1, 2); } static void ShowOne(string title, ref double et) { WriteLine(fmt, title, fst); Dump(0, fst, "{0,-3} "); WriteLine(fm2, Ord(skp), Ord(max)); Dump(skp - 1, max - skp + 1, "{0,4} "); WriteLine("Time taken: {0}ms\n", et = (DateTime.Now - st).TotalMilliseconds); } static BI factorial(int n) { BI res = 1; if (n < 2) return res; while (n > 0) res *= n--; return res; } static bool WTisPrimeSA(int n) { return ((factorial(n - 1) + 1) % n) == 0; } static BI[] facts; static void initFacts(int n) { facts = new BI[n]; facts[0] = facts[1] = 1; for (int i = 1, j = 2; j < n; i = j++) facts[j] = facts[i] * j; } static bool WTisPrime(int n) { return ((facts[n - 1] + 1) % n) == 0; } static void Main(string[] args) { st = DateTime.Now; BI f = 1; for (int n = 2; lst.Count < max; f *= n++) if ((f + 1) % n == 0) lst.Add(n); ShowOne(ms1, ref et1); st = DateTime.Now; int lmt = lst.Last(); lst.Clear(); BitArray flags = new BitArray(lmt + 1); for (int n = 2; n <= lmt; n+=n==2?1:2) if (!flags[n]) { lst.Add(n); for (int k = n * n, n2=n<<1; k <= lmt; k += n2) flags[k] = true; } ShowOne(ms2, ref et2); WriteLine("{0} was {1:0.0} times slower than the {2}.", ms1, et1 / et2, ms2); WriteLine("\n" + ms1 + " stand-alone computation:"); WriteLine("factorial computed for each item"); st = DateTime.Now; for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrimeSA(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); WriteLine("factorials precomputed up to highest item"); st = DateTime.Now; initFacts(lst[max - 1]); for (int x = lst[skp - 1]; x <= lst[max - 1]; x++) if (WTisPrime(x)) Write("{0,4} ", x); WriteLine(); WriteLine("\nTime taken: {0}ms\n", (DateTime.Now - st).TotalMilliseconds); } }
fn factorial_mod(mut n: u32, p: u32) -> u32 { let mut f = 1; while n != 0 && f != 0 { f = (f * n) % p; n -= 1; } f } fn is_prime(p: u32) -> bool { p > 1 && factorial_mod(p - 1, p) == p - 1 } fn main() { println!(" n | prime?\n------------"); for p in vec![2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659] { println!("{:>3} | {}", p, is_prime(p)); } println!("\nFirst 120 primes by Wilson's theorem:"); let mut n = 0; let mut p = 1; while n < 120 { if is_prime(p) { n += 1; print!("{:>3}{}", p, if n % 20 == 0 { '\n' } else { ' ' }); } p += 1; } println!("\n1000th through 1015th primes:"); let mut i = 0; while n < 1015 { if is_prime(p) { n += 1; if n >= 1000 { i += 1; print!("{:>3}{}", p, if i % 16 == 0 { '\n' } else { ' ' }); } } p += 1; } }
Convert this Java snippet to Rust and keep its semantics consistent.
import java.math.BigInteger; public class PrimaltyByWilsonsTheorem { public static void main(String[] args) { System.out.printf("Primes less than 100 testing by Wilson's Theorem%n"); for ( int i = 0 ; i <= 100 ; i++ ) { if ( isPrime(i) ) { System.out.printf("%d ", i); } } } private static boolean isPrime(long p) { if ( p <= 1) { return false; } return fact(p-1).add(BigInteger.ONE).mod(BigInteger.valueOf(p)).compareTo(BigInteger.ZERO) == 0; } private static BigInteger fact(long n) { BigInteger fact = BigInteger.ONE; for ( int i = 2 ; i <= n ; i++ ) { fact = fact.multiply(BigInteger.valueOf(i)); } return fact; } }
fn factorial_mod(mut n: u32, p: u32) -> u32 { let mut f = 1; while n != 0 && f != 0 { f = (f * n) % p; n -= 1; } f } fn is_prime(p: u32) -> bool { p > 1 && factorial_mod(p - 1, p) == p - 1 } fn main() { println!(" n | prime?\n------------"); for p in vec![2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659] { println!("{:>3} | {}", p, is_prime(p)); } println!("\nFirst 120 primes by Wilson's theorem:"); let mut n = 0; let mut p = 1; while n < 120 { if is_prime(p) { n += 1; print!("{:>3}{}", p, if n % 20 == 0 { '\n' } else { ' ' }); } p += 1; } println!("\n1000th through 1015th primes:"); let mut i = 0; while n < 1015 { if is_prime(p) { n += 1; if n >= 1000 { i += 1; print!("{:>3}{}", p, if i % 16 == 0 { '\n' } else { ' ' }); } } p += 1; } }