Sierpiński conjecture

In 1960 Wacław Sierpiński (1882-1969) proved the following interesting result:

Theorem: There exist infinitely many odd integers k such that k2n+1 is composite for every integer n1.

A multiplier k with this property is called a Sierpiński number ( The Sierpiński problem consists in determining the smallest Sierpiński number. In 1962, John Selfridge discovered the Sierpiński number k=78557, which is now believed to be in fact the smallest such number.

Conjecture: The integer k=78557 is the smallest Sierpiński number.

To prove the conjecture, it would be sufficient to exhibit a prime k2n+1 for each k<78557.

Title Sierpiński conjecture
Canonical name SierpinskiConjecture
Date of creation 2013-03-22 13:34:16
Last modified on 2013-03-22 13:34:16
Owner yark (2760)
Last modified by yark (2760)
Numerical id 12
Author yark (2760)
Entry type Conjecture
Classification msc 11B83
Synonym Sierpinski conjectureMathworldPlanetmath