Prime Gap Conjectures

Prime Gap Conjectures by Thomas McClure I

Introduction

This paper is on Prime Gap Conjectures. II

Prime Gap Conjectures

[1] lim{n,%} = {p_{n+1}-p_n} = log p_n lim{n,%} = {p_{n+1}-p_n} = ln p_n/ln 10 log p_n *1.5 == ln p_n/1.5 [2] prime gap g_n = {p_(n+1) – p_n} {p_(n+1) - p_n} < p_{n+1} < p_n^{1 + 1/n} p_n < p_n^{1 + 1/n} ln (p_n) < {1 + 1/n} (ln (p_n) 1 < {1 + 1/n} [3] [p_{n+1} - p_n < p_n] [g_n < p_n] [g_n < root{p_n} < 2*root{p_n} + 1] [g_n < root{p_n}[2 + root{p_n}/2] [g_n < root{p_n} < [2 + root{p_n}/2}] [g_n < root{p_n} < p_n]

[4] [p_n{n+1}/p_n]/p_n^(1/n) < 1 p_n{n+1}/p_n < p_n^(1/n) [p_n{n+1}/p_n]^n > p_n

[5] For prime gap : g_n = root{p_n} n > n/ln n > (n+1)^2

III

Conclusion

This paper is on Prime Gap Conjectures. lim{n,%} = {p_{n+1}-p_n} = log p_n {p_(n+1) - p_n} < p_{n+1} < p_n^{1 + 1/n} [g_n < root{p_n} < p_n] [p_n{n+1}/p_n]^n > p_n g_n = root{p_n}

Restatement: [g_n < root{p_n} < p_n < p_{n+1}

Proof: g_n < 1

< 1.4