Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Every odd perfect number has a prime factor which exceeds $\mathrm{10^{6}}$

Author(s): Peter Hagis Jr.; Graeme L. Cohen.
Journal: Math. Comp. 67 (1998), 1323-1330.
MSC (1991): Primary 11A25, 11Y70
MathSciNet review: 1484897
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Abstract: It is proved here that every odd perfect number is divisible by a prime greater than $10^{6}$ .

References:

1.: A. S. Bang, Taltheoretiske Undersøgelser, Tidsskrift Math. 5, IV (1886), 70-80, 130-137.
2.: M. S. Brandstein, New lower bound for a factor of an odd perfect number, Abstracts of the Amer. Math. Soc. 3 (1982), 257.
3.: J. T. Condict, On an Odd Perfect Number's Largest Prime Divisor, Senior Thesis (Middlebury College), May 1978.
4.: P. Hagis, Jr. and W. L. McDaniel, On the largest prime divisor of an odd perfect number. II, Math. Comp. 29 (1975), 922-924. MR 51:8021
5.: P. Hagis, Jr. and G. L. Cohen, Every odd perfect number has a prime factor which exceeds $10^{6}$ (with appendix), Research Report No.93-5 (School of Mathematical Sciences, University of Technology, Sydney), July 1993.
6.: W. L. McDaniel, On multiple prime divisors of cyclotomic polynomials, Math. Comp. 28 (1974), 847-850. MR 52:8022
7.: P. L. Montgomery, New solutions of $a^{p-1}\equiv 1 \text{ \rm (mod $p^{2}$)}$ , Math. Comp. 61 (1993), 361-363. MR 94d:11003
8.: T. Nagell, Introduction to Number Theory, second edition, Chelsea, New York, 1964. MR 30:4714
9.: I. Niven, Irrational Numbers, Wiley, New York, 1956. MR 18:195c

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