{
  "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"
  }
}