## A New Sieve for the Twin Primes ( How the Number of Twin Primes is Related to the Number of Primes)

**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.

**Download:** **PDF**

### Submission history

[v1] 2018-04-24 16:44:53

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