Saturday, March 14, 2009

Sierpinski numbers

A Sierpinski number is an odd positive integer k such that all integers of the form k2n + 1 (with n taking positive integer values) are composite. In [1], Sierpinski showed that there are infinitely many k with this property. The "Sierpinski problem" asks:
" What is the smallest Sierpinski number ? "
It is conjectured that the answer is k = 78557 (the fact that 78557 is a Sierpinski number was discovered in 1962 by John Selfridge).

Waclaw Sierpinski was born on March 14, 1882 in Warsaw.
[1] Sierpiński, Waclaw "Sur un problème concernant les nombres k2n + 1." Elemente der Mathematik 15, 73-74 (1960).