Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

Pace P. Nielsen

Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

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arxiv math/0602485 v1 pith:YDQ2TZGK submitted 2006-02-22 math.NT

Pace P. Nielsen This is my paper · ORCID

classification math.NT

keywords distinctleastperfectprimefactorsninenumbersavoids

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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.

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Certified Minimal-Prime Branch Closures for Odd Perfect Numbers
math.GM 2026-07 conditional novelty 6.5 of 10

Relative to frozen certificate release C-small-2026-07, no odd perfect number has minimal prime divisor in {5,7,11,13,17}.

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