Polignac's Conjecture with New Prime Number Theorem | OMICS International | Abstract
ISSN: 2090-0902

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## Polignac's Conjecture with New Prime Number Theorem

YinYue Sha*

Dongling Engineering Center, Ningbo Institute of Technology, Zhejiang University, China

*Corresponding Author:
YinYue Sha
Dongling Engineering Center
Ningbo Institute of Technology
Zhejiang University, China
Tel: 571 8517 2244
E-mail: [email protected]

Received Date: July 04, 2016; Accepted Date: November 08, 2016; Published Date: November 11, 2016

Citation: Sha YY (2016) Polignac's Conjecture with New Prime Number Theorem. J Phys Math 7:201. doi: 10.4172/2090-0902.1000201

Copyright: © 2016 Sha YY. 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.

### Abstract

There are infinitely many pairs of consecutive primes which differ by even number En.Let Po(N, En) be the number of Polignac Prime Pairs (which difference by the even integer En) less than an integer (N+En), Pei be taken over the odd prime divisors of the even integer En less than √(N+En), Pni be taken over the odd primes less than √(N+En) except Pei, Pi be taken over the odd primes less than √(N+En), then exists the formulas as follows:

Po(N, En) ≥ INT {N × (1-1/2) × Π (1-1/Pei) × Π (1-2/Pni)} - 1

≥ INT {Ctwin × Ke(N) × 2N/(Ln (N+En))^2} - 1

Po(N, 2) ≥ INT {0.660 × 1.000 × 2N/(Ln (N+2))^2} - 1

Π (Pi(Pi-2)/(Pi-1)^2) ≥ Ctwin=0.6601618158…

Ke(N)=Π( (1-1/Pei)/(1-2/Pei))=Π( (Pei-1)/(Pei-2)) ≥ 1

where -1 is except the natural integer 1.

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