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 ,"*Math. Comp.*, v. 33, 1979, pp. 1333-1336. MR**537979 (80h:10009)****[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]**R. P. Brent & J. M. Pollard, "Factorization of the eighth Fermat number,"*Math. Comp.*, v. 36, 1981, pp. 627-630. MR**606520 (83h:10014)****[6]**G. V. Cormack & H. C. Williams, "Some very large primes of the form ,"*Math. Comp.*, v. 35, 1980, pp. 1419-1421. MR**583519 (81i:10011)****[7]**Gary B. Gostin, "A factor of ,"*Math. Comp.*, v. 35, 1980, pp. 975-976. MR**572869 (81f:10010)****[8]**John C. Hallyburton, Jr. & John Brillhart, "Two new factors of Fermat numbers,"*Math. Comp.*, v. 29, 1975, pp. 109-112. For a correction, see*Math. Comp.*, v. 30, 1976, p. 198. MR**0369225 (51:5460)****[9]**Peter Montgomery, Personal communication.**[10]**Hiromi Suyama, "Searching for prime factors of Fermat numbers with a microcomputer,"*BIT*(Japanese), v. 13, 1981, pp. 240-245. MR**610300 (82c:10012)****[11]**Hiromi Suyama, Personal Communication; published with permission.**[12]**H. C. Williams, "Primality testing on a computer,"*Ars Combin.*, v. 5, 1978, pp. 127-185. MR**504864 (80d:10002)**

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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