New Cullen primes

Abstract

Numbers of the forms C n = n ⋅ 2 n + 1 {C_n} = n \cdot {2^n} + 1 and W n = n ⋅ 2 n − 1 {W_n} = n\cdot {2^n} - 1 are both called Cullen numbers. New primes C n {C_n} are presented for n = 4713 , 5795 , 6611 , 18496 n = 4713,5795,6611,18496 . For W n {W_n} , several new primes are listed, the largest one having n = 18885 n = 18885 . Furthermore, all efforts made to factorize numbers C n {C_n} and W n {W_n} are described, and the result, the complete factorization for all n ≤ 300 n \leq 300 , is given in a Supplement.