High Quality Content by WIKIPEDIA articles! In number theory, a Sierpinski number is an odd natural number k such that integers of the form k2n + 1 are composite (i.e. not prime) for all natural numbers n. In other words, when k is a Sierpinski number, all members of the following set are composite:The number 78,557 was proved to be a Sierpinski number by John Selfridge in 1962, who showed that all numbers of the form 78557·2n+1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}. For another known Sierpinski number, 271129, the covering set is {3, 5, 7, 13, 17, 241}. All currently known Sierpinski numbers possess similar covering sets.In 1967, Sierpi?ski and Selfridge conjectured that 78,557 is the smallest Sierpinski number, and thus the answer to the Sierpinski problem.

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