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Some large primes and amicable numbers


Author: W. Borho
Journal: Math. Comp. 36 (1981), 303-304
MSC: Primary 10A40; Secondary 10A25
DOI: https://doi.org/10.1090/S0025-5718-1981-0595068-2
MathSciNet review: 595068
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Abstract | References | Similar Articles | Additional Information

Abstract: Some new large primes of the form $ 3 \cdot {2^n} - 1$ and $ 9 \cdot {2^n} - 1$, related to amicable numbers, are given. Two new large amicable number pairs are found by the method of so-called "Thabit rules".


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

  • [1] W. Borho, "On Thabit ibn Kurrah's formula for amicable numbers," Math. Comp., v. 26, 1972, pp. 571-578. MR 0313177 (47:1732)
  • [2] H. Riesel, "Lucasian criteria for the primality of $ N = h \cdot {2^n} - 1$," Math. Comp., v. 23, 1969, pp. 869-875. MR 0262163 (41:6773)
  • [3] D. Slowinski, "Searching for the 27th Mersenne prime," J. Recreational Math., v. 11, 1979, pp. 258-261. MR 536930 (80g:10013)
  • [4] M. Souissi, Un Texte Manuscrit d'Ibn Al-Bann$ \vec{a}$ Al-Marrakusi sur les Nombres Parfaits, Abondants Deficients et Amiables, published by Hamdard Nat. Found., Pakistan, Karachi, 1975.
  • [5] H. te Riele, "Four large amicable pairs," Math. Comp., v. 28, 1974, pp. 309-312. MR 0330033 (48:8372)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1981-0595068-2
Article copyright: © Copyright 1981 American Mathematical Society

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