---
pretty_name: Prime List from 1 to 1e14
tags:
- mathematics
- prime-numbers
- parquet
configs:
- config_name: default
  data_files:
  - split: train
    path: "1-1e14/*.parquet"
---

# Prime List from 1 to 1e14

## Purpose

This dataset publishes an ordered list of prime numbers in Parquet format for
streaming, selective shard downloads, and online preview. It contains prime
values only; it does not include labels, natural-language content, or derived
features.

## Coverage and shard contract

- Coverage: `1 <= p < 100,000,000,000,000` (`1e14`)
- Data directory: `1-1e14/`
- Number of shards: 1,000
- Integer interval width per shard: `100,000,000,000` (`1e11`)
- File name pattern: `part-NNNN-of-1000.parquet`
- Shard indices: `0000` through `0999`

Shard `i` contains every prime in the half-open interval
`[i * 1e11, (i + 1) * 1e11)`. The first shard therefore starts with `2`.
Adjacent shard intervals do not overlap and do not leave gaps.

Reading all 1,000 files in file-name order produces the complete globally
sorted list. The dataset is complete when every shard from
`part-0000-of-1000.parquet` through `part-0999-of-1000.parquet` is present.

## Schema

Each file is a directly readable Parquet file with the following schema:

| Column | Arrow type | Nullable | Ordering |
| --- | --- | --- | --- |
| `prime` | `uint64` | No | Strictly increasing |

Parquet data pages use ZSTD compression. A prime appears exactly once in the
shard responsible for its numeric interval.

## Usage

Use streaming mode with Hugging Face Datasets to avoid downloading the entire
collection at once:

```python
from datasets import load_dataset

primes = load_dataset(
    "lzray/primelist",
    data_files="1-1e14/*.parquet",
    split="train",
    streaming=True,
)

for row in primes.take(10):
    print(row["prime"])
```

For a limited numeric range, select only the files whose shard intervals
intersect that range.

## Scope limitations

This repository provides prime enumeration data, not a primality-testing API
or an interactive calculator. Consumers should preserve the `uint64` type;
converting large values to a 32-bit integer will overflow.