Six new factors of Fermat numbers

Authors:
Gary B. Gostin and Philip B. McLaughlin

Journal:
Math. Comp. **38** (1982), 645-649

MSC:
Primary 10-04; Secondary 10A25

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645680-8

MathSciNet review:
645680

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Abstract | References | Similar Articles | Additional Information

Abstract: A new prime factor is given for each of the Fermat numbers , , , , , and . A summary of search limits and recent results is included.

**[1]**A. O. L. Atkin & N. W. Rickert, "Some factors of Fermat numbers,"*Abstracts Amer. Math. Soc.*, v. 1, 1980, p. 211.**[2]**Robert Baillie,*New primes of the form 𝑘⋅2ⁿ+1*, Math. Comp.**33**(1979), no. 148, 1333–1336. MR**537979**, https://doi.org/10.1090/S0025-5718-1979-0537979-0**[3]**Robert Baillie, Personal communication via S. S. Wagstaff, Jr.**[4]**R. P. Brent, "Factorization of the eighth Fermat number,"*Abstracts Amer. Math. Soc.*, v. 1, 1980, p. 565.**[5]**Richard P. Brent and John M. Pollard,*Factorization of the eighth Fermat number*, Math. Comp.**36**(1981), no. 154, 627–630. MR**606520**, https://doi.org/10.1090/S0025-5718-1981-0606520-5**[6]**G. V. Cormack and H. C. Williams,*Some very large primes of the form 𝑘⋅2^{𝑚}+1*, Math. Comp.**35**(1980), no. 152, 1419–1421. MR**583519**, https://doi.org/10.1090/S0025-5718-1980-0583519-8**[7]**Gary B. Gostin,*A factor of 𝐹₁₇*, Math. Comp.**35**(1980), no. 151, 975–976. MR**572869**, https://doi.org/10.1090/S0025-5718-1980-0572869-7**[8]**John C. Hallyburton Jr. and John Brillhart,*Two new factors of Fermat numbers*, Math. Comp.**29**(1975), 109–112. Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday. MR**0369225**, https://doi.org/10.1090/S0025-5718-1975-0369225-1**[9]**Peter Montgomery, Personal communication.**[10]**Hiromi Suyama,*Searching for prime factors of Fermat numbers with a microcomputer*, BIT (Tokyo)**13**(1981), no. 3, 240–245 (Japanese). MR**610300****[11]**Hiromi Suyama, Personal Communication; published with permission.**[12]**H. C. Williams,*Primality testing on a computer*, Ars Combin.**5**(1978), 127–185. MR**504864**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645680-8

Keywords:
Fermat numbers,
factorization

Article copyright:
© Copyright 1982
American Mathematical Society