HMMT 十一月 2011 · 冲刺赛 · 第 34 题
HMMT November 2011 — Guts Round — Problem 34
题目详情
英文原题
[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 max/braceleftbigg/floorleftbigg 60/parenleftbigg1 3−/vextendsingle/vextendsingle/vextendsingle/vextendsingleln/parenleftbiggA d/parenrightbigg/vextendsingle/vextendsingle/vextendsingle/vextendsingle/parenrightbigg/floorrightbigg ,0/bracerightbigg , where Ais your answer and dis the actual answer.
解析
英文解析
- [ 20 ] The integer 843301 is prime. The primorial of a prime number p , denoted p #, is defined to bethe 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 dwhere 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.