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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 F_n(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 · 2^m+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 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.