Stirling Numbers of the Second Kind and Primality
نویسندگان
چکیده
A Stirling number of the second kind is a combinatorial function which yields interesting number theoretic properties with regard to primality. The Stirling number of the second kind, S(n; k) = 1 k! k P i=0 ( 1) k i (k i), counts the number of partitions of an n-element set into k non-empty subsets. A Stirling prime (of the second kind) is a prime p such that p = S(n; k) for some integers n and k. The relationship between Mersenne primes and Stirling primes will be shown. Divisibility theorems with regard to primality will be stated and used to devise algorithms for accelerated searching of Stirling primes. Search results for 1 n 100000 and 1 k 6 will be presented.
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