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A lower bound for the set of odd perfect numbers


Author: Peter Hagis
Journal: Math. Comp. 27 (1973), 951-953
MSC: Primary 10A25; Secondary 10-04
DOI: https://doi.org/10.1090/S0025-5718-1973-0325507-9
MathSciNet review: 0325507
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Abstract: It is proved here that if n is odd and perfect, then $ n > {10^{50}}$.


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

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  • [2] P. Hagis, Jr., & W. L. McDaniel, "On the largest prime divisor of an odd perfect number," Math. Comp., v. 27, 1973, 955-957. MR 0325508 (48:3855)
  • [3] H.-J. Kanold, "Folgerungen aus dem Vorkommen einer Gauss'schen Primzahl in der Primfaktorenzerlegung einer ungeraden vollkommenen Zahl," J. Reine Angew. Math., v. 186, 1944, pp. 25-29. MR 6, 255. MR 0012079 (6:255c)
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  • [6] T. Nagell, Introduction to Number Theory, Wiley, New York; Almqvist & Wiksell, Stockholm, 1951. MR 13, 207. MR 0043111 (13:207b)
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  • [8] C. Pomerance, "Odd perfect numbers are divisible by at least 7 distinct primes," Notices Amer. Math. Soc., v. 19, 1972, pp. A622-A623. Abstract #696-10-5.
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  • [11] B. Tuckerman, "A search procedure and lower bound for odd perfect numbers." Math. Comp., v. 27, 1973, 943-949. MR 0325506 (48:3853)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0325507-9
Article copyright: © Copyright 1973 American Mathematical Society

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