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Old 2007-12-09, 12:52   #46
robert44444uk
 
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Jun 2003
Oxford, UK

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Some notes from unpublished work by Prof Caldwell

Definition of a Sierpinski number

An integer k > 1 is a Sierpinski number base b if gcd(k+1,b-1) = 1 and
k.bn+1 is composite for all n > 0.
• gcd(k+1,b-1) = 1 avoids trivial covers (1-covers).
• k > 1 avoids leading Generalized Fermat divisors. (May use Strong Sierpinski for GFN’s included, and may toss out further GFN’s in the weak case above.)
• n > 0 avoids removing k = p-1 as a multiplier for all primes p and all bases b. (Shouldn’t b be involved in the choice of k?)
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