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SM Journal of Biometrics & Biostatistics

Gauss Riemann Shayinyue Prime Number Distribution Theorem

[ ISSN : 2573-5470 ]

Abstract
Details

Received: 30-Aug-2018

Accepted: 14-Sep-2018

Published: 19-Sep-2018

Research Article | Volume 3 - Issue 3 | Article DOI :

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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

Keywords

Taking Integer; Prime Number; Sieve Method; Prime Number Theorem; Riemann Hypothesis

Abstract

Let Pi(N) be the number of primes less than or equal to N, Pi (2≤Pi≤Pm) be taken over the primes less than or equal to √N, then exists the formula as follows: Pi(N) = INT { N×∏ (1-1/Pi) } + m-1 = Li (N) - 0.5×Li (N^0.5) ± 0.5×Li (N^0.5) Li (N^0.5) ≥ Li (N) - Pi (N) ≥ 0 : ( The Riemann Hypothesis is proved ) Pi (N) = R (N) + K × (Li (N) - R (N) ), 1 ≥ K ≥ -1 . P (K) = 1.99471140200716338969973029967…×EXP (-12.5×K×K) Where the INT { } expresses the taking integer operation of formula spread out type in { }, the Li (N) is the logarithmic integral function, the R (N) is the Riemann Prime Counting Function, the P (K) is the Normal Distribution N (μ=0,σ=0.2).

Citation

Sha YY. Gauss Riemann Shayinyue Prime Number Distribution Theorem. SM J Biometrics Biostat. 2018; 3(3): 1035.