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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 BR98
 A. Björn and H. Riesel, "Factors of generalized Fermat numbers," Math. Comp., 67 (1998) 441446. MR 98e:11008
Abstract:
A search for prime factors of the generalized Fermat numbers F_{n}(a,b)=a^{2n}+b^{2n} has been carried out for all pairs (a,b) with a,b< 12 and gcd(a,b)=1. The search k limit on the factors, which all have the form p=k · 2^{m}+1, was k=10^{9} for m< 100 and k=3 · 10^{6} for 101< m < 1000. Many larger primes of this form have also been tried as factors of F_{n}(a,b). Several thousand new factors were found, which are given in our tables. For the smaller of the numbers, i.e. for n< 15, or, if a,b< 8, for n< 16, 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 n < 7 are now completely factored.
