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Outline of a proof that every odd perfect number has at least eight prime factors


Author: Peter Hagis
Journal: Math. Comp. 35 (1980), 1027-1032
MSC: Primary 10A20
DOI: https://doi.org/10.1090/S0025-5718-1980-0572873-9
MathSciNet review: 572873
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Abstract | References | Similar Articles | Additional Information

Abstract: An argument is outlined which demonstrates that every odd perfect number is divisible by at least eight distinct primes.


References [Enhancements On Off] (What's this?)

  • [1] E. Z. CHEIN, "Non-existence of odd perfect numbers of the form $ q_1^{{a_1}}q_2^{{a_2}} \cdots q_6^{{a_6}}$ and $ {5^{{a_1}}}q_2^{{a_2}} \cdots q_9^{{a_9}}$ (Unpublished manuscript.)
  • [2] P. HAGIS, JR., "If n is odd and perfect then $ n > {10^{45}}$. A case study proof with a supplement in which the lower bound is improved to $ {10^{50}}$." (Copy deposited in UMT file.)
  • [3] P. HAGIS, JR., "Every odd perfect number has at least eight prime factors." (Copy deposited in UMT file.)
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1980-0572873-9
Article copyright: © Copyright 1980 American Mathematical Society

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