Definition:Sierpiński Number
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Definition
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 elements of the set:
- $\set {k 2^n + 1}$
are composite.
Source of Name
This entry was named for Wacław Franciszek Sierpiński.