Odd Perfect Numbers Have At Least Nine Distinct Prime Factors
arXiv:math/0602485 · doi:10.1090/S0025-5718-07-01990-4
Abstract
An odd perfect number, N, is shown to have at least nine distinct prime factors. If 3 does not divide N, then N must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.
17 pages