Prime p₀= 1236575468144108567 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 70 2 28 2 88 2 28 2 70 2 (?)
a_n: 0 2 72 74 102 104 192 194 222 224 294 296
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: 296
Found by: Cruncher Pete
db: batch=77, k=12, 2 70 2 28 2 88

SPT(16)	1236574248906299441	0 20 32 66 90 116 140 222 230 312 336 362 386 420 432 452	-1219237809126
SPT(16)	1236574518460795847	0 6 20 36 56 90 224 246 320 342 476 510 530 546 560 566	-949683312720
SPT(16)	1236574578002878363	0 6 54 58 84 118 168 198 226 256 306 340 366 370 418 424	-890141230204
STPT(10)	1236574662114238157	0 2 60 62 72 74 84 86 144 146	-806029870410
SPT(16)	1236574884813955529	0 24 38 62 84 104 108 138 164 194 198 218 240 264 278 302	-583330153038
SPT(16)	1236575284102509787	0 10 46 72 106 112 130 172 210 252 270 276 310 336 372 382	-184041598780
TPT(14)	1236575781365168471	0 2 6 8 36 38 78 80 108 110 120 122 168 170	313221059904
STPT(10)	1236575838481757831	0 2 30 32 78 80 126 128 156 158	370337649264
SPT(16)	1236576447671032621	0 46 102 136 142 186 196 222 226 252 262 306 312 346 402 448	979526924054
SPT(16)	1236577393089308561	0 30 42 62 96 98 120 128 180 188 210 212 246 266 278 308	1924945199994
SPT(16)	1236577429409830769	0 20 60 62 104 114 132 144 158 170 188 198 240 242 282 302	1961265722202