Odd perfect numbers have a prime factor exceeding 10⁸

Goto, Takeshi; Ohno, Yasuo

doi:10.1090/S0025-5718-08-02050-4

Odd perfect numbers have a prime factor exceeding $10^8$
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by Takeshi Goto and Yasuo Ohno;

Math. Comp. 77 (2008), 1859-1868

DOI: https://doi.org/10.1090/S0025-5718-08-02050-4

Published electronically: February 12, 2008

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Abstract:

Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding $10^7$. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding $10^8$.

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