Number Theory


A Sieve for the Twin Primes

Authors: H. L. Mitchell

This paper presents a sieve for the twin primes using a double application of the Sieve of Eratosthenes to the k index for multiples of 6 centered around the primes ranging from 5 to sqrt N. Considering the set {(6k-1, 6k+1)}, we look at the exact pattern in which multiples of primes p occur in the set with respect to the values of k. By deleting the values of k such that 6k-1 is composite, we get the set of all pairs such that 6k-1 is prime, then from these we delete those in which 6k+1 is composite. That leaves us with the set of all twin primes less than N. We derive a mathematical formula accordingly using the Euler product formula, the Prime Number Theorem, Mertens’ Theorem and the Hardy-Littlewood Conjecture. The main results are: 1) A sieve for the twin primes similar to the sieve of Eratosthenes for primes 2) A formula for the approximate number of twin primes less than N in terms of the number of primes 3) The asymptotic formula for the number of twin primes less than N

Comments: 14 Pages.

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Submission history

[v1] 2017-04-26 17:54:24

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