Factorization of the eighth Fermat number

Authors:
Richard P. Brent and John M. Pollard

Journal:
Math. Comp. **36** (1981), 627-630

MSC:
Primary 10A25; Secondary 10-04, 65C05

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606520-5

MathSciNet review:
606520

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Abstract | References | Similar Articles | Additional Information

Abstract: We describe a Monte Carlo factorization algorithm which was used to factorize the Fermat number . Previously was known to be composite, but its factors were unknown.

**[1]**R. P. Brent, "An improved Monte Carlo factorization algorithm," BIT, v. 20, 1980, pp. 176-184. MR**583032 (82a:10007)****[2]**J. C. Hallyburton & J. Brillhart, "Two new factors of Fermat numbers,"*Math. Comp.*, v. 29, 1975, pp. 109-112. MR**0369225 (51:5460)****[3]**M. A. Morrison & J. Brillhart, "A method of factoring and the factorization of ,"*Math. Comp.*, v. 29, 1975, pp. 183-208. MR**0371800 (51:8017)****[4]**J. M. Pollard, "A Monte Carlo method for factorization,"*BIT*, v. 15, 1975, pp. 331-334. MR**50**#6992. MR**0392798 (52:13611)****[5]**J. M. Pollard, "Monte Carlo methods for index computation ,"*Math. Comp.*, v. 32, 1978, pp. 918-924. MR**52**#13611. MR**0491431 (58:10684)****[6]**M. Rabin, "Probabilistic algorithms,"*Algorithms and Complexity*(J. F. Traub, Ed.), Academic Press, New York, 1976, pp. 31-40. MR**0464678 (57:4603)****[7]**H. C. Williams & J. S. Judd, "Some algorithms for prime testing using generalized Lehmer functions,"*Math. Comp.*, v. 30, 1976, pp. 867-886. MR**0414473 (54:2574)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606520-5

Keywords:
Fermat numbers,
factorization,
Monte Carlo methods

Article copyright:
© Copyright 1981
American Mathematical Society