Odd perfect numbers not divisible by $3$ are divisible by at least ten distinct primes
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- by Masao Kishore PDF
- Math. Comp. 31 (1977), 274-279 Request permission
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.References
- Carl Pomerance, Odd perfect numbers are divisible by at least seven distinct primes, Acta Arith. 25 (1973/74), 265–300. MR 340169, DOI 10.4064/aa-25-3-265-300
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- Peter Hagis Jr. and Wayne L. McDaniel, On the largest prime divisor of an odd perfect number. II, Math. Comp. 29 (1975), 922–924. MR 371804, DOI 10.1090/S0025-5718-1975-0371804-2 M. BUXTON & S. ELMORE, "An extension of lower bounds for odd perfect numbers," Notices Amer. Math. Soc., v. 23, 1976, p. A-55. Abstract #731-10-40.
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 274-279
- MSC: Primary 10A20
- DOI: https://doi.org/10.1090/S0025-5718-1977-0429716-3
- MathSciNet review: 0429716