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

Sequence of Known Riesel Numbers
It is conjectured that $509203$ is the smallest Riesel number.

However, there are smaller candidates that are still being checked.

Also see

 * Riesel Problem
 * Sierpiński Number

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