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Two new factors of Fermat numbers


Authors: John C. Hallyburton and John Brillhart
Journal: Math. Comp. 29 (1975), 109-112
MSC: Primary 10-04; Secondary 10A40
DOI: https://doi.org/10.1090/S0025-5718-1975-0369225-1
Corrigendum: Math. Comp. 30 (1976), 198.
Corrigendum: Math. Comp. 30 (1976), 198.
MathSciNet review: 0369225
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Abstract | References | Similar Articles | Additional Information

Abstract: A new prime factor is given for each of the Fermat numbers $ {F_{12}}$ and $ {F_{13}}$ (none was previously known for $ {F_{13}}$). The factoring method used and its machine implementation are discussed. A short table of factors and a current status list are also included.


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

  • [1] JOHN BRILLHART, "Some miscellaneous factorizations," Math. Comp., v. 17, 1963, pp. 447-450.
  • [2] ALEXANDER HURWITZ & J. L. SELFRIDGE, "Fermat numbers and perfect numbers," Notices Amer. Math. Soc., v. 8, 1961, p. 601, Abstract #587-104.
  • [3] MICHAEL A. MORRISON & JOHN BRILLHART, "The factorization of $ {F_7}$," Bull. Amer. Math. Soc., v. 77, 1971, p. 264. MR 42 #3012. MR 0268113 (42:3012)
  • [4] MICHAEL A. MORRISON & JOHN BRILLHART, "A method of factoring and the factorization of $ {F_7}$," Math. Comp., v. 29, 1975, pp. 183-205 (this issue). MR 0371800 (51:8017)
  • [5] G. A. PAXSON, "The compositeness of the thirteenth Fermat number," Math. Comp., v. 15, 1961, p. 420. MR 23 #A1578. MR 0124264 (23:A1578)
  • [6] HANS RIESEL, "A factor of the Fermat number $ {F_{19}}$," Math. Comp., v. 17, 1963, p. 458.
  • [7] RAPHAEL M. ROBINSON, "Mersenne and Fermat numbers," Proc. Amer. Math. Soc., v. 5, 1954, pp. 842-846. MR 16, 335. MR 0064787 (16:335d)
  • [8] RAPHAEL M. ROBINSON, "Factors of Fermat numbers," MTAC, v. 11, 1957, pp. 21-22. MR 19, 14. MR 0085269 (19:14e)
  • [9] RAPHAEL M. ROBINSON, "A report on primes of the form $ k \bullet {2^n} + 1$ and on factors of Fermat numbers," Proc. Amer. Math. Soc., v. 9, 1958, pp. 673-681. MR 20 #3097. MR 0096614 (20:3097)
  • [10] J. L. SELFRIDGE, "Factors of Fermat numbers," MTAC, v. 7, 1953, pp. 274-275.
  • [11] J. L. SELFRIDGE & ALEXANDER HURWITZ, "Fermat numbers and Mersenne numbers," Math. Comp., v. 18, 1964, pp. 146-148. MR 28 #2991. MR 0159775 (28:2991)
  • [12] CLAUDE P. WRATHALL, "New factors of Fermat numbers," Math. Comp., v. 18, 1964, pp. 324-325. MR 29 #1167. MR 0163868 (29:1167)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0369225-1
Keywords: Fermat numbers, factoring
Article copyright: © Copyright 1975 American Mathematical Society

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