HMMT 十一月 2011 · 冲刺赛 · 第 34 题
HMMT November 2011 — Guts Round — Problem 34
题目详情
- [ 20 ] The integer 843301 is prime. The primorial of a prime number p , denoted p #, is defined to be the product of all prime numbers less than or equal to p . Determine the number of digits in 843301#. Your score will be ∣ {⌊ ( ( )∣ )⌋ } ∣ ∣ 1 A ∣ ∣ max 60 − ln , 0 , ∣ ∣ 3 d where A is your answer and d is the actual answer.
解析
- [ 20 ] The integer 843301 is prime. The primorial of a prime number p , denoted p #, is defined to be the product of all prime numbers less than or equal to p . Determine the number of digits in 843301#. Your score will be ∣ {⌊ ( ( )∣ )⌋ } ∣ ∣ 1 A ∣ ∣ max 60 − ln , 0 , ∣ ∣ 3 d where A is your answer and d is the actual answer. Answer: 365851 Remark: 843301# − 1 is the largest known prime number of the form p # − 1, where p is prime.