Hi,
I generated a list of all the primes in the first 1billion digits, then counted the spacing between all the primes, and got this result:
"name" is the spacing between consecutive primes, and "result" is the count of how many times that spacing occurred, as you can see from the below, the spacing of 6 is the most common gap between primes, and also there is an oscillation of the spacing, where multiples of 6 spacings always have more primes.
ie for name=6 that is the count of all the primes in the first 1billion digits of numbers with a prime spacing of 6.
How do you explain that there are these peaks in the prime distribution on multiples of 6
There is a nice curve that the distribution of primes generates as well from this data.
{ Name = 1, Count = 1 } { Name = 2, Count = 3424506 } { Name = 4, Count = 3424679 } { Name = 6, Count = 6089791 } { Name = 8, Count = 2695109 } { Name = 10, Count = 3484767 } { Name = 12, Count = 4468957 } { Name = 14, Count = 2464565 } { Name = 16, Count = 1846097 } { Name = 18, Count = 3351032 } { Name = 20, Count = 1824043 } { Name = 22, Count = 1569679 } { Name = 24, Count = 2367474 } { Name = 26, Count = 1119585 } { Name = 28, Count = 1219243 } { Name = 30, Count = 2177991 } { Name = 32, Count = 683896 } { Name = 34, Count = 719531 } { Name = 36, Count = 1171524 } { Name = 38, Count = 548746 } { Name = 40, Count = 648780 } { Name = 42, Count = 954456 } { Name = 44, Count = 389634 } { Name = 46, Count = 334720 } { Name = 48, Count = 577247 } { Name = 50, Count = 328066 } { Name = 52, Count = 245804 } { Name = 54, Count = 410754 } { Name = 56, Count = 211462 } { Name = 58, Count = 181948 } { Name = 60, Count = 371839 } { Name = 62, Count = 115558 } { Name = 64, Count = 118951 } { Name = 66, Count = 216787 } { Name = 68, Count = 88396 } { Name = 70, Count = 125564 } { Name = 72, Count = 126663 } { Name = 74, Count = 62526 } { Name = 76, Count = 55113 } { Name = 78, Count = 105313 } { Name = 80, Count = 53522 } { Name = 82, Count = 37982 } { Name = 84, Count = 78077 } { Name = 86, Count = 27793 } { Name = 88, Count = 28878 } { Name = 90, Count = 58057 } { Name = 92, Count = 19282 } { Name = 94, Count = 17669 } { Name = 96, Count = 31078 } { Name = 98, Count = 16175 } { Name = 100, Count = 16900 } { Name = 102, Count = 22393 } { Name = 104, Count = 10310 } { Name = 106, Count = 8719 } { Name = 108, Count = 15459 } { Name = 110, Count = 9065 } { Name = 112, Count = 7139 } { Name = 114, Count = 10892 } { Name = 116, Count = 4710 } { Name = 118, Count = 4502 } { Name = 120, Count = 9621 } { Name = 122, Count = 2975 } { Name = 124, Count = 3136 } { Name = 126, Count = 5863 } { Name = 128, Count = 2043 } { Name = 130, Count = 2813 } { Name = 132, Count = 3510 } { Name = 134, Count = 1487 } { Name = 136, Count = 1297 } { Name = 138, Count = 2589 } { Name = 140, Count = 1516 } { Name = 142, Count = 953 } { Name = 144, Count = 1555 } { Name = 146, Count = 668 } { Name = 148, Count = 724 } { Name = 150, Count = 1486 } { Name = 152, Count = 506 } { Name = 154, Count = 583 } { Name = 156, Count = 798 } { Name = 158, Count = 306 } { Name = 160, Count = 360 } { Name = 162, Count = 534 } { Name = 164, Count = 247 } { Name = 166, Count = 182 } { Name = 168, Count = 443 } { Name = 170, Count = 198 } { Name = 172, Count = 158 } { Name = 174, Count = 255 } { Name = 176, Count = 128 } { Name = 178, Count = 106 } { Name = 180, Count = 200 } { Name = 182, Count = 80 } { Name = 184, Count = 89 } { Name = 186, Count = 101 } { Name = 188, Count = 33 } { Name = 190, Count = 63 } { Name = 192, Count = 74 } { Name = 194, Count = 32 } { Name = 196, Count = 41 } { Name = 198, Count = 73 } { Name = 200, Count = 28 } { Name = 202, Count = 23 } { Name = 204, Count = 46 } { Name = 206, Count = 13 } { Name = 208, Count = 18 } { Name = 210, Count = 48 } { Name = 212, Count = 12 } { Name = 214, Count = 11 } { Name = 216, Count = 15 } { Name = 218, Count = 6 } { Name = 220, Count = 12 } { Name = 222, Count = 11 } { Name = 224, Count = 6 } { Name = 226, Count = 6 } { Name = 228, Count = 3 } { Name = 230, Count = 3 } { Name = 232, Count = 1 } { Name = 234, Count = 13 } { Name = 236, Count = 5 } { Name = 238, Count = 1 } { Name = 240, Count = 5 } { Name = 242, Count = 4 } { Name = 244, Count = 2 } { Name = 246, Count = 4 } { Name = 248, Count = 4 } { Name = 250, Count = 4 } { Name = 252, Count = 1 } { Name = 260, Count = 1 } { Name = 276, Count = 1 } { Name = 282, Count = 1 }
cheers, Jamie