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We note that one more factor is missing from Table 1 in Bjorn-Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441 446, in addition to the three already reported upon in Bjorn-Riesel, Table errata to \"Factors of generalized Fermat numbers\", Math. Comp. 74 (2005), p. 2099.

We note that one more factor is missing from Table 1 in Bjorn-Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441 446, in addition to the three already reported upon in Bjorn-Riesel, Table errata to \"Factors of generalized Fermat numbers\", Math. Comp. 74 (2005), p. 2099.

We note that one more factor is missing from Table 1 in Björn–Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441–446, in addition to the three already reported upon in Björn–Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), p. 2099.

We note that three factors are missing from Table 1 in Factors of generalized Fermat numbers by A. Björn and H. Riesel published in Math. Comp. 67 (1998), 441–446.

We note that three factors are missing from Table 1 in Factors of generalized Fermat numbers by A. Bjorn and H. Riesel published in Math. Comp. 67 (1998), 441-446.

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.

Let vi = v2i-1 - 2 with v0 given. If $v_{n - 2} \\equiv 0 (\\operatorname{mod} N)$ is a necessary and sufficient criterion that N = h · 2n - 1 be prime, this is called a Lucasian criterion for the primality of N. Many such criteria are known, but the case h = 3A has not been treated in full generality earlier. A theorem is proved that (by aid of computer) enables the effective determination of suitable numbers v0 for any given N, if $h < 2^n$. The method is used on all N in the domain h = 3(6)105, n ≤ 1000. The Lucasian criteria thus constructed are applied, and all primes N = h · 2n - 1 in the domain are tabulated.

Let v i = v i − 1 2 − 2 vi = v_i - 1^2 - 2 with v 0 v_0 given. If v n − 2 ≡ 0 ( mod N ) v_n - 2 0( N) is a necessary and sufficient criterion that N = h ⋅ 2 n − 1 N = h 2^n - 1 be prime, this is called a Lucasian criterion for the primality of N N . Many such criteria are known, but the case h = 3 A h = 3A has not been treated in full generality earlier. A theorem is proved that (by aid of computer) enables the effective determination of suitable numbers v 0 v_0 for any given N N , if h > 2 n h > 2^n . The method is used on all N N in the domain h = 3 ( 6 ) 105 , n ≦ 1000 h = 3(6)105,n 1000 . The Lucasian criteria thus constructed are applied, and all primes N = h ⋅ 2 n − 1 N = h 2^n - 1 in the domain are tabulated.