Prime Path Ratio

Using the letters ‘A’ and ‘B’ to denote the start and finish points of where Twin Primes could occur, we can show the possible path of all Prime gaps as being either ‘A’ or ‘B’. By showing these in a doughnut chart we can compare the ratio of the four groups. Interesting there is more or less an even distribution of Prime numbers which take up the ‘A’ or ‘B’ position. However, as soon as we start to look at the subsequent Prime number position we see a definite alternating pattern, so a Prime in the ‘A’ position is more likely to be followed by a Prime in the ‘B’ position and vice versa. It is less likely for chains of AA or BB to appear. At first this may seem to contradict what is known about the frequency of Prime gaps. We know that 6 is the most frequent Prime gap but this gap size belongs to the smaller AA and BB groups. However, as they share the same gap sizes, we have to combine the two groups to get the correct frequency. AB and BA groups are approximately 30% each, but the AA and BB group combined are 40% of all Prime gaps, making them the largest group, which may help to explain why 6 is the most frequent Prime gap size.

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