## On The Consecutive Integers n+i-1 = (i+1)P_{i}

**Authors:** Chun-Xuan Jiang

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

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 7 Apr 2009

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