A proof of the twin prime conjecture

2017/06/26 by Theophilus Agama, Agama, Theophilus
Mathematics · #Mathematics and Applications #History and Theory of Mathematics #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1707.03265

Abstract

In this paper, we prove the twin prime conjecture showing that ∑ _\substackp≤ x
p,p+2∈ ℙ1≥ (1+o(1))(x)/(2Clog² x)where C:=C(2)>0 fixed and ℙ is the set of all prime numbers. In particular, it implies ∑ _{p,p+2∈ ℙ}1=\inftywhen we take x\longrightarrow ∞ on both sides of the inequality. We start by developing a general method for estimating correlations of the form ∑ _{n≤ x}G(n)G(n+l)for a fixed 1≤ l≤ x and where G:ℕ\longrightarrow ℝ⁺.

Related

• The area method and applications
• Correlations of Almost Primes
• A Positive Lower Bound for the Sum of Log-Reciprocal Twin Prime Products via Weighted Sieve
• Some history about Twin Prime Conjecture
• Proof of the Twin Prime Conjecture (Together with the Proof of Polignac's Conjecture for Cousin Primes)