Factors of generalized Fermat numbers
Authors:
Anders Björn and Hans Riesel
Journal:
Math. Comp. 67 (1998), 441446
MSC (1991):
Primary 1104, 11A51, 11Y05, 11Y11
Erratum:
Math. Comp. 74 (2005), 2099
Erratum:
Math. Comp. 80 (2011), 18651866
Supplement:
Additional information related to this article.
MathSciNet review:
1433262
Fulltext PDF Free Access
Abstract 
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Abstract: A search for prime factors of the generalized Fermat numbers has been carried out for all pairs with and GCD. The search limit on the factors, which all have the form , was for and for . Many larger primes of this form have also been tried as factors of . Several thousand new factors were found, which are given in our tables.For the smaller of the numbers, i.e. for , or, if , for , the cofactors, after removal of the factors found, were subjected to primality tests, and if composite with , searched for larger factors by using the ECM, and in some cases the MPQS, PPMPQS, or SNFS. As a result all numbers with are now completely factored.
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Additional Information
Anders Björn
Affiliation:
Department of Mathematics, Linköping University, S581 83 Linköping, Sweden
Email:
anbjo@mai.liu.se
Hans Riesel
Affiliation:
Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S100 44 Stockholm, Sweden
Email:
riesel@nada.kth.se
DOI:
http://dx.doi.org/10.1090/S0025571898008916
PII:
S 00255718(98)008916
Keywords:
Fermat numbers,
primes,
factorization
Received by editor(s):
May 6, 1996
Received by editor(s) in revised form:
September 19, 1996
Article copyright:
© Copyright 1998
American Mathematical Society
