Have You Noticed the Symmetry of Primes in the Sieve of Eratosthenes?

[r2i]

just got dumped out and lost my thread, so will keep this brief and add later once accepeted

www.primepatterns.wordpress.com

anyone noticed the symmetry of primes (well pseudoprimes if you must) starting at each p#/2 i.e. 105, 1155, 15015?

they arise from the Sieve of Erathosthenes and give good explanations of prime distributions and patterns

 

[CRGreathouse]

If I understand you correctly, Dirichlet proved that 'symmetry' in 1837.

 

[r2i]

I thought there was some similarity, just couldn't bridge the gap. So why is the 6n-1, 6n+1 framework mentioned so regularly whilst the next step (sorry for the lack of formatting - it's coloured and formatted on the website):

-14 31 61 151 181 211
-8 37 67 97 127 157
-4 11 41 71 101 131 191
-2 13 43 73 103 163 193 line of symmetry at 15-45-90-120-165-195
+2 17 47 107 137 167 197
+4 19 79 109 139 199
+8 23 53 83 113 173
+14 29 59 89 149 179

is mentioned much less (the matching locations for pairs are of passing interest) and the general trend not at all, although all sorts of papers are produced attempting to show patterns in gaps between primes?