Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The factorization of the ninth Fermat number


Authors: A. K. Lenstra, H. W. Lenstra, M. S. Manasse and J. M. Pollard
Journal: Math. Comp. 61 (1993), 319-349
MSC: Primary 11Y05; Secondary 11Y40
Addendum: Math. Comp. 64 (1995), 1357.
MathSciNet review: 1182953
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we exhibit the full prime factorization of the ninth Fermat number $ {F_9} = {2^{512}} + 1$. It is the product of three prime factors that have 7, 49, and 99 decimal digits. We found the two largest prime factors by means of the number field sieve, which is a factoring algorithm that depends on arithmetic in an algebraic number field. In the present case, the number field used was $ {\mathbf{Q}}(\sqrt[5]{2})$. The calculations were done on approximately 700 workstations scattered around the world, and in one of the final stages a supercomputer was used. The entire factorization took four months.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11Y05, 11Y40

Retrieve articles in all journals with MSC: 11Y05, 11Y40


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1182953-4
PII: S 0025-5718(1993)1182953-4
Keywords: Fermat number, factoring algorithm
Article copyright: © Copyright 1993 American Mathematical Society