Definition:Riesel Number

A Riesel number is an odd positive integer $k$ such that integers of the form $k2^n - 1$ are composite for all positive integers $n$.

The list of known Riesel numbers is found here:

It is conjectured that $509\203$ is the smallest Riesel number, however there are $50$ smaller candidates that are still being checked.

Also see

 * Sierpiński Number