
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The sigma function of a positive integer n is the sum of the positive divisors of n. This is usually denoted using the greek letter , but for those with nongraphical browsers we will use sigma(n) on these pages. Here are the first few values of the sigma function:
Clearly, for primes p, sigma(p)=p+1. sigma(x) is a multiplicative function, so its value can be determined from its value at the prime powers:
Example: sigma(2000) = sigma(2^{4}5^{3}) = sigma(2^{4})^{.}sigma(5^{3}) = (2^{5}1)/(21) ^{.} (5^{4}1)/(51) = 31 ^{.} 156 = 4836.
Chris K. Caldwell © 19992019 (all rights reserved)
