|
Odd perfect numbers have a prime factor exceeding 
Author(s):
Paul
M.
Jenkins.
Journal:
Math. Comp.
72
(2003),
1549-1554.
MSC (2000):
Primary 11A25, 11Y70
Posted:
January 8, 2003
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is proved that every odd perfect number is divisible by a prime greater than  .
References:
-
- 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
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(2000):
11A25, 11Y70
Retrieve articles in all Journals with MSC
(2000):
11A25, 11Y70
Additional Information:
Paul
M.
Jenkins
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email:
pmj5@math.byu.edu
DOI:
10.1090/S0025-5718-03-01496-0
PII:
S 0025-5718(03)01496-0
Received by editor(s):
November 7, 2001
Posted:
January 8, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Nielsen, Pace P., An upper bound for odd perfect numbers, Integers, posted on 10/22/2003 (electronic). (English) MR MR2036480
|
Comments: webmaster@ams.org