Two new factors of Fermat numbers
HTML articles powered by AMS MathViewer
- by John C. Hallyburton and John Brillhart PDF
- Math. Comp. 29 (1975), 109-112 Request permission
Corrigendum: Math. Comp. 30 (1976), 198.
Corrigendum: Math. Comp. 30 (1976), 198.
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
- JOHN BRILLHART, "Some miscellaneous factorizations," Math. Comp., v. 17, 1963, pp. 447-450.
ALEXANDER HURWITZ & J. L. SELFRIDGE, "Fermat numbers and perfect numbers," Notices Amer. Math. Soc., v. 8, 1961, p. 601, Abstract #587-104.
- Michael A. Morrison and John Brillhart, The factorization of $F_{7}$, Bull. Amer. Math. Soc. 77 (1971), 264. MR 268113, DOI 10.1090/S0002-9904-1971-12711-8
- Michael A. Morrison and John Brillhart, A method of factoring and the factorization of $F_{7}$, Math. Comp. 29 (1975), 183โ205. MR 371800, DOI 10.1090/S0025-5718-1975-0371800-5
- G. A. Paxson, The compositeness of the thirteenth Fermat number, Math. Comp. 15 (1961), 420. MR 124264, DOI 10.1090/S0025-5718-1961-0124264-0 HANS RIESEL, "A factor of the Fermat number ${F_{19}}$," Math. Comp., v. 17, 1963, p. 458.
- Raphael M. Robinson, Mersenne and Fermat numbers, Proc. Amer. Math. Soc. 5 (1954), 842โ846. MR 64787, DOI 10.1090/S0002-9939-1954-0064787-4
- Raphael M. Robinson, Factors of Fermat numbers, Math. Tables Aids Comput. 11 (1957), 21โ22. MR 85269, DOI 10.1090/S0025-5718-1957-0085269-0
- Raphael M. Robinson, A report on primes of the form $k\cdot 2^{n}+1$ and on factors of Fermat numbers, Proc. Amer. Math. Soc. 9 (1958), 673โ681. MR 96614, DOI 10.1090/S0002-9939-1958-0096614-7 J. L. SELFRIDGE, "Factors of Fermat numbers," MTAC, v. 7, 1953, pp. 274-275.
- J. L. Selfridge and Alexander Hurwitz, Fermat numbers and Mersenne numbers, Math. Comp. 18 (1964), 146โ148. MR 159775, DOI 10.1090/S0025-5718-1964-0159775-8
- Claude P. Wrathall, New factors of Fermat numbers, Math. Comp. 18 (1964), 324โ325. MR 163868, DOI 10.1090/S0025-5718-1964-0163868-9
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 109-112
- MSC: Primary 10-04; Secondary 10A40
- DOI: https://doi.org/10.1090/S0025-5718-1975-0369225-1
- MathSciNet review: 0369225