Odd perfect numbers have a prime factor exceeding

Author:
Paul M. Jenkins

Journal:
Math. Comp. **72** (2003), 1549-1554

MSC (2000):
Primary 11A25, 11Y70

DOI:
https://doi.org/10.1090/S0025-5718-03-01496-0

Published electronically:
January 8, 2003

MathSciNet review:
1972752

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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that every odd perfect number is divisible by a prime greater than .

**1.**A. Bang,*Taltheoretiske undersøgelser*, Tidsskrift Math.**5 IV**(1886), 70-80, 130-137.**2.**M. Brandstein,*New lower bound for a factor of an odd perfect number*, Abstracts Amer. Math. Soc.**3**(1982), 257, 82T-10-240.**3.**R. P. Brent, G. L. Cohen, and H. J. J. te Reile,*Improved techniques for lower bounds for odd perfect numbers*, Mathematics of Computation**57**(1991), 857-868. MR**92c:11004****4.**E. Chein,*An odd perfect number has at least 8 prime factors*, Ph.D. thesis, Pennsylvania State University, 1979.**5.**J. Condict,*On an odd perfect number's largest prime divisor*, Senior Thesis, Middlebury College, 1978.**6.**P. Hagis, Jr.,*Outline of a proof that every odd perfect number has at least eight prime factors*, Mathematics of Computation**35**(1980), 1027-1032. MR**81k:10004****7.**P. Hagis, Jr. and G. L. Cohen,*Every odd perfect number has a prime factor which exceeds*, Mathematics of Computation**67**(1998), 1323-1330. MR**98k:11002****8.**P. Hagis, Jr. and W. McDaniel,*On the largest prime divisor of an odd perfect number II*, Mathematics of Computation**29**(1975), 922-924. MR**51:8021****9.**D. E. Iannucci,*The second largest prime divisor of an odd perfect number exceeds ten thousand*, Mathematics of Computation**68**(1999), 1749-1760. MR**2000i:11200****10.**-,*The third largest prime divisor of an odd perfect number exceeds one hundred*, Mathematics of Computation**69**(2000), 867-879. MR**2000i:11201****11.**Paul M. Jenkins,*Odd perfect numbers have a prime factor exceeding*, Senior Thesis, Brigham Young University, 2000.**12.**T. Nagell,*Introduction to number theory*, second ed., Chelsea, New York, 1964. MR**30:4714****13.**C. Pomerance,*Odd perfect numbers are divisible by at least seven distinct primes*, Acta. Arith.**25**(1974), 265-300, MR**49:4925**

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Additional Information

**Paul M. Jenkins**

Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602

Email:
pmj5@math.byu.edu

DOI:
https://doi.org/10.1090/S0025-5718-03-01496-0

Received by editor(s):
November 7, 2001

Published electronically:
January 8, 2003

Article copyright:
© Copyright 2003
American Mathematical Society