Number Theory


Can the Twin Prime Conjecture be Proven

Authors: James Edwin Rock

Let P_n be the n_th prime. For twin primes P_n – P_(n-1) = 2. Let X be the number of (6j –1, 6j+1) pairs in the interval [P_n, P_n^2]. The number of twin primes (TPAn) in [P_n, P_n^2] can be approximated by the formula (a_3 /5)(a_4 /7)(a_5 /11)…(a_n /P_n)(X) for 3 ≤ m ≤ n, a_m = P_m –2 . We establish a lower bound for TPAn (3/5)(5/7)(7/9)…(P_n–2)/P_n)(X) = 3X/P_n < TPAn. We exhibit a formula showing as P_n increases, the number of twin primes in the interval [P_n, P_n^2] also increases. Let P_n – P_(n-1) = c. For all n (TPAn-1)(1+(2c –2)/2P_(n-1)+(c^2–2c)/2P_(n-1)^2) < TPAn

Comments: 7 Pages.

Download: PDF

Submission history

[v1] 2019-02-01 10:53:12
[v2] 2019-02-13 08:29:18
[v3] 2019-02-16 12:01:31
[v4] 2019-02-19 08:32:39
[v5] 2019-03-04 08:20:36
[v6] 2019-03-29 12:35:08 (removed)
[v7] 2019-04-24 08:52:05 (removed)
[v8] 2019-06-04 10:28:14

Unique-IP document downloads: 60 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