New Cullen Primes

Abstract

Numbers of the forms C"=-2" + l and W" = n-2" -\ are both called Cullen numbers. New primes C" are presented for n = 4713 , 5795 , 6611 , 18496 . For Wn , several new primes are listed, the largest one having n = 18885 . Furthermore, all efforts made to factorize numbers Cn and W" are described, and the result, the complete factorization for all n < 300, is given in a Supplement.