## Counting numbers with at least four distinct prime factors less than 100

### Problem 268

Published on Friday, 11th December 2009, 05:00 pm; Solved by 919; Difficulty rating: 70%It can be verified that there are 23 positive integers less than 1000 that are divisible by at least four distinct primes less than 100.

Find how many positive integers less than 10^{16} are divisible by at least four distinct primes less than 100.