## Proof of the Twin Prime Conjecture

**Authors:** James Edwin Rock

Let P_n be the n_th prime. For twin primes P_n – P_n-1 = 2. We exhibit formula for calculating the number of twin primes in the closed interval [P_n, P_n^2]. We prove that as P_n increases the number of twin primes in the interval [P_n, Pn^2] also increases.

**Comments:** 5 Pages. This replacement paper adds a ratio TPA / 2.06 column to Table 2 and Table 1 contains a comparison of the twin prime pairs formula for [743,743^2] and [19993,19993^2]. It gives a better explanation for the twin prime pairs formula.

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### Submission history

[v1] 2018-12-31 14:29:57

[v2] 2019-01-07 12:49:24

[v3] 2019-01-14 10:52:26

[v4] 2019-01-22 09:05:33

[v5] 2019-01-25 15:03:02

[v6] 2019-01-30 16:38:19

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