
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) A function f(n) defined on the positive integers is completely multiplicative if f(nm)=f(n)f(m) for all pairs n and m (compare this with multiplicative functions). Three simple examples are f(n)=0, f(n)=1, and f(n)=n^{c} (for a fixed positive value c). If f(n) is multiplicative and we factor n into distinct primes as n=p_{1}^{a1}^{.} p_{2}^{a2}^{.} ...^{.}p_{k}^{ak}, then f(n) = f(p_{1})^{a1}^{.} f(p_{2})^{a2}^{.} ...^{.}f(p_{k})^{ak}.
Chris K. Caldwell © 19992019 (all rights reserved)
