Number Theory


A Fifth Smarandache Friendly Prime Pair

Authors: Philip Gibbs

A Smarandache friendly prime pair (SFPP) is a pair of prime numbers (p,q), p < q, such that the product pq is equal to the sum of all primes from p to q inclusive. Previously four such pairs were known: (2,5), (3,13), (5,31) and (7,53). Now a fifth one is found by a brute force computer search. A heuristic approximation can be to estimate the expected number of SFPPs in a given interval. The result suggests that the probability of further pairs existing is about 0.07.

Comments: 4 pages

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Submission history

[v1] 28 Apr 2010
[v2] 30 Apr 2010
[v3] 2 May 2010
[v4] 4 May 2010

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