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

Journal of Physical Mathematics
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Research Article Open Access

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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Author(s): YinYue Sha

Keywords

Twin prime, Polignac prime, Bilateral sieve method, Physical Mathematics, Axioms, Topology, Integration , Algebraic Geometry, Quantum Mechanics, mirror symmetry, Noether's theorem, Quantumelectrodynamics, Hamilton Mechanics, vector bundle, Riemannian Geometry, Theory of Mathematical Modeling, Fourier Analysis, Theoretical Physics, Analytical Geometry, Differential Equations, Complex Analysis.

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