Factors of generalized fermat numbers

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 limit k 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 n ≤ 11, 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.