Six new factors of Fermat numbers
Authors:
Gary B. Gostin and Philip B. McLaughlin
Journal:
Math. Comp. 38 (1982), 645649
MSC:
Primary 1004; Secondary 10A25
MathSciNet review:
645680
Fulltext PDF Free Access
Abstract 
References 
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Abstract: A new prime factor is given for each of the Fermat numbers , , , , , and . A summary of search limits and recent results is included.
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𝑘⋅2ⁿ+1, Math. Comp.
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Robert Baillie, Personal communication via S. S. Wagstaff, Jr.
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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
(81i:10011), http://dx.doi.org/10.1090/S00255718198005835198
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𝐹₁₇, Math. Comp.
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C. Williams, Primality testing on a computer, Ars Combin.
5 (1978), 127–185. MR 504864
(80d:10002)
 [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. 13331336. 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. 627630. MR 606520 (83h:10014)
 [6]
 G. V. Cormack & H. C. Williams, "Some very large primes of the form ," Math. Comp., v. 35, 1980, pp. 14191421. MR 583519 (81i:10011)
 [7]
 Gary B. Gostin, "A factor of ," Math. Comp., v. 35, 1980, pp. 975976. MR 572869 (81f:10010)
 [8]
 John C. Hallyburton, Jr. & John Brillhart, "Two new factors of Fermat numbers," Math. Comp., v. 29, 1975, pp. 109112. 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. 240245. 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. 127185. MR 504864 (80d:10002)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206456808
PII:
S 00255718(1982)06456808
Keywords:
Fermat numbers,
factorization
Article copyright:
© Copyright 1982
American Mathematical Society
