Frequency Distribution of Gaps between Consecutive Prime Num

[Mblacob]

Frequency Distribution of Gaps between Consecutive Prime Numbers

For the experiment nine sequences (sets) of consecutive Primes numbers were generated.
Set #1 includes 1,500 Prime numbers, and others 1,000 Prime numbers for each.

Set 1 - Initial Prime Number = 7
Set 2 - Initial Prime Number = 990,918,479
Set 3 - Initial Prime Number = 999,999,131
Set 4 - Initial Prime Number = 1,054,223,369
Set 5 - Initial Prime Number = 2,019,169,299,698,041
Set 6 - Initial Prime Number = 20,000,000,000.700,000,389
Set 7 - Initial Prime Number = 2,999,999,999,999,999,999,999,999,999,999,999,917,867
Set 8 - Initial Prime Number = 999...999...999...910000149 (79 digits)
Set 9 - Initial Prime Number = 999...999...999...999910000057 (128 digits)

Set 1 - Median Gap = 6, Max Gap = 36, 95% Gap = 20
Set 2 - Median Gap = 14-16, Max Gap = 132, 95% Gap = 58
Set 3 - Median Gap = 14-16, Max Gap = 152, 95% Gap = 58
Set 4 - Median Gap = 14-16, Max Gap = 112, 95% Gap = 54
Set 5 - Median Gap = 26, Max Gap = 196, 95% Gap = 100
Set 6 - Median Gap = 28-30, Max Gap = 294, 95% Gap = 130
Set 7 - Median Gap = 68, Max Gap = 612, 95% Gap = 266
Set 8 - Median Gap = 126, Max Gap = 990, 95% Gap = 540-542
Set 9 - Median Gap = 210, Max Gap = 1870, 95% Gap = 926

1. In each set distribution of gaps between Prime numbers is asymmetric.
2. Each set has different characteristic compare to others (looks like sets 2,3, and 4 can be combined in one).
3. There is obvious trend exists in increasing Median Gaps, 95% Gaps, and Max.Gaps as well.

I can provide all details about data involved in this experiment to everybody who is interested to interpret and discuss
this matter.

[Guest]

This problem is an opened one. Even the twin problem is not solved.

[Mblacob]

Frequency Distribution of Gaps between Consecutive Prime Numbers

For the experiment nine sequences (sets) of consecutive Primes numbers were generated.
Set #1 includes 1,500 Prime numbers, and others 1,000 Prime numbers for each.

Set 1 - Initial Prime Number = 7
Set 2 - Initial Prime Number = 990,918,479
Set 3 - Initial Prime Number = 999,999,131
Set 4 - Initial Prime Number = 1,054,223,369
Set 5 - Initial Prime Number = 2,019,169,299,698,041
Set 6 - Initial Prime Number = 20,000,000,000.700,000,389
Set 7 - Initial Prime Number = 2,999,999,999,999,999,999,999,999,999,999,999,917,867
Set 8 - Initial Prime Number = 999...999...999...910000149 (79 digits)
Set 9 - Initial Prime Number = 999...999...999...999910000057 (128 digits)

Set 1 - Median Gap = 6, Max Gap = 36, 95% Gap = 20
Set 2 - Median Gap = 14-16, Max Gap = 132, 95% Gap = 58
Set 3 - Median Gap = 14-16, Max Gap = 152, 95% Gap = 58
Set 4 - Median Gap = 14-16, Max Gap = 112, 95% Gap = 54
Set 5 - Median Gap = 26, Max Gap = 196, 95% Gap = 100
Set 6 - Median Gap = 28-30, Max Gap = 294, 95% Gap = 130
Set 7 - Median Gap = 68, Max Gap = 612, 95% Gap = 266
Set 8 - Median Gap = 126, Max Gap = 990, 95% Gap = 540-542
Set 9 - Median Gap = 210, Max Gap = 1870, 95% Gap = 926

1. In each set distribution of gaps between Prime numbers is asymmetric.
2. Each set has different characteristic compare to others (looks like sets 2,3, and 4 can be combined in one).
3. There is obvious trend exists in increasing Median Gaps, 95% Gaps, and Max.Gaps as well.

I can provide all details about data involved in this experiment to everybody who is interested to interpret and discuss
this matter.

[Guest]

This problem is an opened one. Even the twin problem is not solved.

I disagree! The twin prime conjecture and the the more general Polignac Conjecture (https://en.wikipedia.org/wiki/Polignac%27s_conjecture) are closed. Both conjectures are true!

Relevant Reference Link:

https://www.quora.com/What-great-conjectures-in-mathematics-combine-additive-theory-of-numbers-with-the-multiplicative-theory-of-numbers