How many primes under 100000000?

There are 5,761,455 prime numbers less than 100,000,000 according to the Prime number Theorem, which estimates the distribution of prime numbers. This theorem states that the density of primes around a large number n is approximately 1/ln(n). Therefore, the number of primes under 100,000,000 can be estimated by dividing 100,000,000 by the natural logarithm of 100,000,000, which is approximately 5,761,455.