I have taken 2 sets: The first is a consecutive list of the first prime of twin pairs. The second is a consecutive list of numbers as follow 1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+4+5 ....
I have then compared between the lists by dividing the numbers of the second list with the numbers of the first list, and a steady growth rate of distribution occurs (as seen in the pictures below).
If you analyze the data (as seen in the pictures below), you will notice that:
If the fluctuation of column E is too high (usually above 1.1), then the "next" twin pair will have to be smaller than the "current:" pair, thus producing an error.
You can also notice that the fluctuation of column E is never too low (probably not less than 0.99 after the first few hundreds).
The same phenomenon happens if I replace Column C with the squares 1,4,9,16,… or with an arbitrary quadratic polynomial.
When replacing column C with a constant equal to 1, the max value never passes 1 (obviously). However, after the first few hundreds the min value again is probably not less than 0.99
Can anyone provide me with a theoretic explanation for why this might be?.
List of first 100,000 with column C: 1, 1+2, 1+2+3, 1+2+3+4 ....
List of first 100,000 with column C: with the squares 1,4,9,16,25 ...
List of first 100,000 with column C: constant = 1
Thanks.