Definition:Riesel Number

Definition
Let $k$ be an odd positive integer.

Then $k$ is a Riesel number :


 * For all positive integers $n$, the number $k2^n - 1$ is composite

The list of known Riesel numbers starts:
 * $509203, 762701, 777149, 790841, 992077, 1106681$

It is conjectured that $509203$ is the smallest Riesel number, however there are smaller candidates that are still being checked.

Also see

 * Sierpiński Number

He proved in 1956 that there are an infinite number of Riesel numbers.