Number Theory


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

Unique-IP document downloads: 23 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus