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.