Sierpinski number

This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers

Definition

A Sierpinski number is a natural number $k$ such that, for all natural numbers $n$, the number $k\cdot 2^{n}+1$ is composite.

It is known that $78,557$ is a Sierpinski number. The Sierpinski problem asks whether this is the smallest Sierpinski number.

Relation with other properties

• Riesel number: The analogue of Sierpinski number for the expression $k\cdot 2^{n}-1$.