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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Odd perfect numbers not divisible by $ 3$ are divisible by at least ten distinct primes


Author: Masao Kishore
Journal: Math. Comp. 31 (1977), 274-279
MSC: Primary 10A20
MathSciNet review: 0429716
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Abstract: Hagis and McDaniel have shown that the largest prime factor of an odd perfect number N is at least 100111, and Pomerance has shown that the second largest prime factor is at least 139. Using these facts together with the method we develop, we show that if $ 3\nmid N$, N is divisible by at least ten distinct primes.


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DOI: https://doi.org/10.1090/S0025-5718-1977-0429716-3
Article copyright: © Copyright 1977 American Mathematical Society