Number Theory

   

A Sieve for the Twin Primes

Authors: Henry L. Mitchell

We introduce a sieve for the number of twin primes less than N by sieving through the set {k ∊ ℤ+ | 6k < N}. We derive formula accordingly using the Euler product and the Brun. Sieve. We then use the Prime Number Theorem and Mertens’ Theorem. The main results are: 1) A sieve for the twin primes similar to the sieve of Eratosthenes for primes involving only the values of k, the indices of the multiples of 6, ranging over k = p ,5 ≤ p <√N 2) A formula for the approximate number of twin primes less than N in terms of the number of primes less than N 3) The asymptotic formula for the number of twin primes less than N verifying the Hardy Littlewood Conjecture.

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[v1] 2017-10-07 15:48:59

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