
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The number of positive divisors of n is denoted by d(n) (or tau(n) or better, ). Here are the first few values of this function:
Clearly, for primes p, d(p)=2; and for prime powers, d(p^{n})=n+1. For example, 3^{4} has the five (4+1) positive divisors 1, 3, 3^{2}, 3^{3}, and 3^{4}. Since d(x) is a multiplicative function, this is enough to know d(n) for all integers nif the canonical factorization of n is then the number of divisors is = (e_{1}+1)(e_{2}+1)(e_{3}+1) ... (e_{k}+1).For example, 4200 is 2^{3}3^{1}5^{2}7^{1}, so it has (3+1)(1+1)(2+1)(1+1) = 48 positive divisors.
Chris K. Caldwell © 19992020 (all rights reserved)
