Definition:Sierpiński Number

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There are two kinds of Sierpiński number:

Sierpiński Numbers of the First Kind

The Sierpiński numbers of the first kind are the integers $S_n$ in the form:

$S_n := n^n + 1$

for all integers $n$.

Sierpiński Numbers of the Second Kind

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

That is, when $k$ is a Sierpiński number of the second kind, all members of the set:

$\left\{{k 2^n + 1}\right\}$

are composite.

Source of Name

This entry was named for Wacław Franciszek Sierpiński.