Riesel conjecture | Riesel problem

There exist infinitely many odd integers k such that k·2^n - 1 is composite for every n>=1. Numbers k with this property are called Riesel numbers, while analogous numbers with the minus sign replaced by a plus are called Sierpiński numbers of the second kind.

Brier number | Cunningham number | Mersenne number | Sierpiński number of the second kind | Sierpiński's composite number theorem | Thâbit ibn Kurrah rule