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Harvard-MIT November Tournament

Number theory Difficulty 4.6 AIME Find the answer United States

Problem:

The integer 843301843301 is prime. The primorial of a prime number pp, denoted p#p \#, is defined to be the product of all prime numbers less than or equal to pp. Determine the number of digits in 843301#843301\#. Your score will be
max⁡{∣ 60(13−∣ln⁡(Ad)∣)⌋,0}, \left.\max \left\{\left\lvert\, 60\left(\frac{1}{3}-\left|\ln \left(\frac{A}{d}\right)\right|\right)\right.\right\rfloor, 0\right\},
where AA is your answer and dd is the actual answer.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

Answer: 365851365851

Remark: 843301#−1843301\#-1 is the largest known prime number of the form p#−1p\#-1, where pp is prime.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.