# Primo numero 100

While a simple method, trial division quickly becomes impractical for testing large integers because the number of possible factors grows too rapidly as n increases. According to the prime number theorem explained below, the number of prime numbers less than n {\displaystyle {\sqrt {n}}} is approximately given by n / ln ⁡ ( n ) {\displaystyle {\sqrt {n}}/\ln({\sqrt {n}})} , so the algorithm may need up to this number of trial divisions to check the primality of n . For n = 10 20 , this number is 450 million—too large for many practical applications.