Prime p₀= 1115202583108322771 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 76 2 88 2 76 2 58 2 (?)
a_n: 0 2 60 62 138 140 228 230 306 308 366 368
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: 368
Found by: vinn@[CNT]
db: batch=76, k=12, 2 58 2 76 2 88

SPT(16)	1115201536312519987	0 24 36 42 64 94 102 126 130 154 162 192 214 220 232 256	-1046795802784
SPT(16)	1115201685579567143	0 24 68 164 176 204 218 350 354 486 500 528 540 636 680 704	-897528755628
SPT(16)	1115202145956915901	0 10 16 30 40 42 52 106 126 180 190 192 202 216 222 232	-437151406870
TPT(14)	1115202159871960757	0 2 102 104 114 116 240 242 252 254 312 314 384 386	-423236362014
STPT(10)	1115202516142205501	0 2 6 8 48 50 90 92 96 98	-66966117270
SPT(16)	1115202580419162121	0 18 40 42 60 78 138 148 150 160 220 238 256 258 280 298	-2689160650
TPT(14)	1115202668769688271	0 2 48 50 66 68 120 122 168 170 180 182 216 218	85661365500
SPT(16)	1115202935169936469	0 82 114 148 204 262 280 294 358 372 390 448 504 538 570 652	352061613698
STPT(10)	1115203019406891011	0 2 36 38 78 80 120 122 156 158	436298568240
SPT(16)	1115203525232734261	0 16 22 36 46 48 58 70 108 120 130 132 142 156 162 178	942124411490
STPT(10)	1115203962531114431	0 2 66 68 108 110 150 152 216 218	1379422791660