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Solutions of the congruence ap-1 ≡ 1 (mod pr)
A search for double solutions of a p-1 ≡ 1 (mod p 2 ) for primes a, p with 100 2 32 are presented. Expand
New Fibonacci and Lucas primes
We report on a search for new primes Fn and Ln which extends previous work of J. C. Brillhart, H. Williams, and F. Morain. Expand
Factors of generalized Fermat numbers
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 approximatelyExpand
New Cullen primes
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, theExpand
Factors of Fermat numbers and large primes of the form ⋅2ⁿ+1
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 aExpand
Solutions of the congruence a
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 ofExpand