Number Theory


On The Consecutive Integers n+i-1 = (i+1)Pi

Authors: Chun-Xuan Jiang

By using the Jiang's function J2(ω) we prove that there exist infinitely many integers n such that n = 2P1, n+1 = 3P2, ..., n+k-1 = (k+1)Pk are all composites for arbitrarily long k, where P1, P2, ..., Pk are all primes. This result has no prior occurrence in the history of number theory.

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[v1] 7 Apr 2009

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