Generalized Fermat numbers have the form F b,m = b 2m + 1. Their odd prime factors are of the form k . 2 n + 1, k odd, n > m. It is shown that each prime is a factor of some F b,m for approximately… Expand

Numbers of the forms C n = n.2 n + 1 and W n = n.2 n − 1 are both called Cullen numbers. New primes C n are presented for n = 4713, 5795, 6611, 18496. For W n , several new primes are listed, the… Expand

A new factor is given for each of the Fermat numbers F52, F931, F6835, and F9448. In addition, a factor of F75 discovered by Gary Gostin is presented. The current status for all F, is shown in a… Expand

To supplement existing data, solutions of a p−1 ≡ 1 (mod p 2) are tabulated for primes a, p with 100 < a < 1000 and 10 4 < p < 10 11. For a < 100, five new solutions p > 2 32 are presented. One of… Expand