Prime p₀= 2313411568361311589 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 46 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 90 92 120 122 132 134
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 134
Found by: Drago75
db: batch=81, k=12, 2 10 2 28 2 46

SPT(16)	2313408457312942777	0 12 30 46 90 100 120 124 162 166 186 196 240 256 274 286	-3111048368812
SPT(16)	2313409649760828667	0 6 42 60 76 100 102 126 130 154 156 180 196 214 250 256	-1918600482922
STPT(10)	2313409871194107779	0 2 18 20 30 32 42 44 60 62	-1697167203810
SPT(16)	2313410604460871759	0 8 20 110 134 152 158 174 188 204 210 228 252 342 354 362	-963900439830
SPT(16)	2313410877087256147	0 4 6 10 42 60 64 66 130 132 136 154 186 190 192 196	-691274055442
STPT(12)	2313410958928082987	0 2 30 32 42 44 72 74 84 86 114 116	-609433228602
SPT(16)	2313411732881358829	0 108 130 132 150 192 228 264 298 334 370 412 430 432 454 562	164520047240
STPT(12)	2313411768720528767	0 2 30 32 42 44 90 92 102 104 132 134	200359217178
STPT(10)	2313411905359759619	0 2 18 20 30 32 42 44 60 62	336998448030
STPT(10)	2313411967478458547	0 2 30 32 42 44 54 56 84 86	399117146958
TPT(14)	2313412358128428371	0 2 36 38 126 128 138 140 168 170 180 182 216 218	789767116782