A Sierpiński number of the second kind is a number k satisfying Sierpiński's composite number theorem, i.e., a Proth number k such that k·2^n + 1 is composite for every n>=1. The smallest known example is k = 78, 557, proved in 1962 by J. Selfridge, but the fate of a number of smaller candidates remains to be determined before this number can be established as the smallest such number. As of 1996, 35 candidates remained, a number which had been reduced to 17 by the beginning of 2002.
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