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
DOI:
https://doi.org/10.1090/S00255718198206456808
MathSciNet review:
645680
Fulltext PDF Free Access
Abstract  References  Similar Articles  Additional Information
Abstract: A new prime factor is given for each of the Fermat numbers ${F_{29}}$, ${F_{36}}$, ${F_{99}}$, ${F_{147}}$, ${F_{150}}$, and ${F_{201}}$. A summary of search limits and recent results is included.

A. O. L. Atkin & N. W. Rickert, "Some factors of Fermat numbers," Abstracts Amer. Math. Soc., v. 1, 1980, p. 211.
 Robert Baillie, New primes of the form $k\cdot 2^{n}+1$, Math. Comp. 33 (1979), no. 148, 1333โ1336. MR 537979, DOI https://doi.org/10.1090/S00255718197905379790 Robert Baillie, Personal communication via S. S. Wagstaff, Jr. R. P. Brent, "Factorization of the eighth Fermat number," Abstracts Amer. Math. Soc., v. 1, 1980, p. 565.
 Richard P. Brent and John M. Pollard, Factorization of the eighth Fermat number, Math. Comp. 36 (1981), no. 154, 627โ630. MR 606520, DOI https://doi.org/10.1090/S00255718198106065205
 G. V. Cormack and H. C. Williams, Some very large primes of the form $k\cdot 2^{m}+1$, Math. Comp. 35 (1980), no. 152, 1419โ1421. MR 583519, DOI https://doi.org/10.1090/S00255718198005835198
 Gary B. Gostin, A factor of $F_{17}$, Math. Comp. 35 (1980), no. 151, 975โ976. MR 572869, DOI https://doi.org/10.1090/S00255718198005728697
 John C. Hallyburton Jr. and John Brillhart, Two new factors of Fermat numbers, Math. Comp. 29 (1975), 109โ112. MR 369225, DOI https://doi.org/10.1090/S00255718197503692251 Peter Montgomery, Personal communication.
 Hiromi Suyama, Searching for prime factors of Fermat numbers with a microcomputer, BIT (Tokyo) 13 (1981), no. 3, 240โ245 (Japanese). MR 610300 Hiromi Suyama, Personal Communication; published with permission.
 H. C. Williams, Primality testing on a computer, Ars Combin. 5 (1978), 127โ185. MR 504864
Retrieve articles in Mathematics of Computation with MSC: 1004, 10A25
Retrieve articles in all journals with MSC: 1004, 10A25
Additional Information
Keywords:
Fermat numbers,
factorization
Article copyright:
© Copyright 1982
American Mathematical Society