As promised, GIMPS gave $50,000 of the EFF award to the UCLA Department of Mathematics, where Edson Smith was responsible for installing and maintaining the GIMPS software on their computers. Another $25,000 has been donated to a math-related charity selected by GIMPS founder George Woltman. The remaining $25,000 has been paid in GIMPS Mersenne Prime Research Discovery Awards to Odd Magnar Strindmo for his discovery of M47 , Hans-Michael Elvenich for M46 , the University of Central Missouri ( M44 and M43 ), Dr. Martin Nowak ( M42 ), Josh Findley ( M41 ), Michael Shafer and his selected charity ( M40 ) and Michael Cameron ( M39 ).

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.