Newbie
Joined: Apr 2016 From: Arizona Posts: 15 Thanks: 0 
Starting at the beginning, 1,2,3 is the first prime pattern. 1, not a prime, 2 and 3, twin primes (tp). At 2^2, all the even numbers are composite, so the count goes to every,third number is composite. 3^2=9c. 5,7tp. 3*5=15c. 11,13tp. Now the pattern will change every third and fifth number from 15. 3*7=21c. 17,19tp. 5on from 15 s 5^2=25c. 23p. 3*9+27c. No prime between 25 and 27. 3*11=33c. 29,31tp. 5*7 =35c. no prime between 33 and 35. 3on past 33=39c. 37p. 3on past 39 is 45c. 5on from is 45. 3 and 5 meet for a composite so 41, 43tp. 3 and 5 pattern starts again 51c, 55c. But 7^2 enters at 49c, so only 47p and 53p between 45 and 55. 3on from 51 is 57c. 3on from 57 is 63c.7on past 49 is 63c. So 7 and 3 join. This keeps the 3,5 pattern intact through the 60's. 5on past 55 is 65c. 3 past 63 is 69c. 3 past 69 is 75. 5 past 65 is 75. 7 past 63 is 77, so 7 finally enters and up sets the 3,5 pattern. Compare the 20's and the 50's. 21c,51c,23p,53p,25c,55c,27c,57c,29p,59p. 20's and 50's pattern are the same. Compare the 30's and 60's. 31p,61p,33c,63c,35c,65c,37p,67p,39c,69c. Again, the 30's and60's pattern are the same. The 3,5 composite pattern will run the same and meet every 30on. The only change to their pattern is when other primes enter after p^2 and show up again every pon after p^2. 3,5,7 meet at 105c (*35 or 5*21, or 7*15) and run their pattern up to 315c, where they meet again. In those 105on's, 11,13,17 will show up occasionally to upset the pattern and make the primes look random.
