Using this program you can find distribution of prime differences on high number intervals.

Run

To generate csv file with prime frequency make the following steps:

1. Download gmp library of version 6.1.2 and extract here.
2. Make run.sh file executable chmod +x run.sh
3. Execute run script ./run.sh

Research

Following intervals were explored:

1. 2^0, 2^0 + 10^7
2. 2^256, 2^256 + 10^7
3. 2^512, 2^512 + 10^7
4. 2^1024, 2^1024 + 10^7
5. 2^2048, 2^2048 + 10^7

Count of primes

interval	prime count
1	664578
2	56368
3	28234
4	13948
5	7112

Plots

A multiple of six

I noticed a frequency of differences which are multiple of six is significantly more than others. The graph below shows two lines, one has only points that meet the condition difference % 6 == 0 and the second line consists of points that do not.