sierpinskis composite number theorem - Wolfram|Alpha

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Input interpretation

Sierpiński's composite number theorem

Alternate names

Sierpiński problem | Sierpiński's theorem

Definition

As proved by Sierpiński, there exist infinitely many positive odd numbers k such that k·2^n + 1 is composite for every n>=1. Numbers k with this property are called Sierpiński numbers of the second kind, and analogous numbers with the plus sign replaced by a minus are called Riesel numbers. It is conjectured that the smallest value of k for a Sierpiński number of the second kind is k = 78557 (although a handful of smaller candidates remain to be eliminated) and that the smallest Riesel number is k = 509203.

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Related terms

Cunningham number | Proth number | Proth prime | Riesel number | Sierpiński number of the second kind | Sierpiński's prime sequence theorem

Subject classifications

MathWorld

prime representations | unsolved problems

MSC 2010

11N32

Associated person

Wacław Sierpiński

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