global-journal-of-science-frontier-research-f-mathematics-decision Global Journal of Science Frontier Research - F: Mathematics & Decision 0975-5896 2249-4626 Global Journals Publishing Group Incorporated 115860 Twin Prime Number Theorem ShaYinYue CHINA, Zhejiang University 24 10 2017 17 F7

Let Pt(N) be the number of twin primes less than or equal to N, Pi (3 Pi Pm) be taken over the odd primes less than or equal to √N, then exists the formula as follows: Pt(N) ≥ INT { N×(1－1/2)×Π (1－2/Pi) } － 2 ≥ INT { Ct×2N/(Ln (N))^2 } － 2 Pt(N) ≥ INT { 0.660×2N/(Ln (N))^2 } － 2 ≥ 0.660×2N/(Ln (N))^2 － 3 Π ( Pi(Pi－2)/(Pi－1)^2 ) ≥ Ct ＝ 0.6601618158… Where the INT { } expresses the taking integer operation of formula spread out type in { }.

 twin prime bilateral sieve method. Full Text

Let Pt(N) be the number of twin primes less than or equal to N, Pi (3 Pi Pm) be taken over the odd primes less than or equal to √N, then exists the formula as follows: Pt(N) ≥ INT { N×(1－1/2)×Π (1－2/Pi) } － 2 ≥ INT { Ct×2N/(Ln (N))^2 } － 2 Pt(N) ≥ INT { 0.660×2N/(Ln (N))^2 } － 2 ≥ 0.660×2N/(Ln (N))^2 － 3 Π ( Pi(Pi－2)/(Pi－1)^2 ) ≥ Ct ＝ 0.6601618158… Where the INT { } expresses the taking integer operation of formula spread out type in { }.