HMMT 十一月 2008 · 冲刺赛 · 第 36 题
HMMT November 2008 — Guts Round — Problem 36
题目详情
- [ 25 ] How many numbers less than 1 , 000 , 000 are the product of exactly 2 distinct primes? You willreceive b 25 − 50 · | − 1 |c points, if you submit N and the correct answer is A .N
英文原题
[ 25 ] How many numbers less than 1 , 000 , 000 are the product of exactly 2 distinct primes? You will
receive b 25 − 50 · | N
A − 1 |c points, if you submit N and the correct answer is A .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
解析
英文解析
- [ 25 ] How many numbers less than 1 , 000 , 000 are the product of exactly 2 distinct primes? You willreceive b 25 − 50 · | − 1 |c points, if you submit N and the correct answer is A .N
Answer: 209867 While it is difficult to compute this answer without writing a program or using a acalculator, it can be approximated using the fact that the number of primes less than a positive integern is about .nlog n 7