Authors: H.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.It shows the uniform distribution of the pairs (6k-1,6k+1) that are not twin primes and the decreasing frequency of multiples of p as p increases. 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.
Comments: 12 Pages.
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[v1] 2018-04-24 16:44:53
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