On the Consecutive Integers n+i-1=(i+1) PiJiang CX*
Institute for Basic Research, Palm Harbor, P.O. Box 3924, Beijing 100854, P.R. China
- *Corresponding Author:
- Jiang CX
Institute for Basic Research
Palm Harbor, P.O. Box 3924
Beijing 100854, P.R. China
Tel: +1-727-688 3992
E-mail: [email protected]
Received Date: February 23, 2017; Accepted Date: May 16, 2017; Published Date: May 22, 2017
Citation: Jiang CX (2017) On the Consecutive Integers n+i-1=(i+1) Pi. J Generalized Lie Theory Appl 11: 267. doi: 10.4172/1736-4337.1000267
Copyright: © 2017 Jiang CX. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.