| { | |
| "data_source": "DigitalLearningGmbH/MATH-lighteval", | |
| "prompt": [ | |
| { | |
| "role": "user", | |
| "content": "Given a positive integer \\( a \\), define a sequence of integers \\( x_1, x_2, x_3, \\ldots \\) such that \\( x_1 = a \\) and \\( x_{n+1} = 2x_n + 1 \\). Let \\( y_n = 2^{x_n} - 1 \\). Determine the largest possible integer \\( k \\) such that for some positive integer \\( a \\), the numbers \\( y_1, y_2, \\ldots, y_k \\) are all prime numbers. Let's think step by step and output the final answer within \\boxed{}.\nA part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model." | |
| } | |
| ], | |
| "ability": "math", | |
| "reward_model": { | |
| "style": "rule", | |
| "ground_truth": "2" | |
| }, | |
| "extra_info": { | |
| "split": "train", | |
| "index": 9724, | |
| "question": "Given a positive integer \\( a \\), define a sequence of integers \\( x_1, x_2, x_3, \\ldots \\) such that \\( x_1 = a \\) and \\( x_{n+1} = 2x_n + 1 \\). Let \\( y_n = 2^{x_n} - 1 \\). Determine the largest possible integer \\( k \\) such that for some positive integer \\( a \\), the numbers \\( y_1, y_2, \\ldots, y_k \\) are all prime numbers. Let's think step by step and output the final answer within \\boxed{}.\nA part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model.", | |
| "transfer_instruction": "A part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model.", | |
| "difficulty": 0.5, | |
| "difficulty_raw": "4/8", | |
| "dataset": "Polaris-Dataset-53K" | |
| } | |
| } |