Reference Database
(references for the Prime Pages)
The Prime Pages

Home
Search Site

Largest
Finding
How Many?
Mersenne

Glossary

Prime Curios!
e-mail list

FAQ
Prime Lists
Titans

Submit primes
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) 441--446.  MR 98e:11008
Abstract: A search for prime factors of the generalized Fermat numbers Fn(a,b)=a2n+b2n 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 · 2m+1, was k=109 for m< 100 and k=3 · 106 for 101< m < 1000. Many larger primes of this form have also been tried as factors of Fn(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.
Prime Pages' Home
Another prime page by Chris K. Caldwell