Prime p₀= 2378171158000668047 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 88 2 28 2 10 2 28 2 88 2 (?)
a_n: 0 2 90 92 120 122 132 134 162 164 252 254
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: 254
Found by: [SG-2W]Kurzer
db: batch=81, k=12, 2 88 2 28 2 10

SPT(16)	2378170506170778461	0 2 6 62 158 176 200 212 216 228 252 270 366 422 426 428	-651829889586
SPT(16)	2378170547388058853	0 20 26 44 80 86 104 126 134 156 174 180 216 234 240 260	-610612609194
SPT(16)	2378170558893968231	0 26 32 42 60 98 150 228 260 338 390 428 446 456 462 488	-599106699816
STPT(10)	2378170720163380691	0 2 6 8 48 50 90 92 96 98	-437837287356
STPT(10)	2378170907682542639	0 2 42 44 60 62 78 80 120 122	-250318125408
SPT(16)	2378171059473006877	0 36 66 76 112 150 162 190 282 310 322 360 396 406 436 472	-98527661170
SPT(16)	2378171550631117069	0 10 30 48 52 58 72 78 112 118 132 138 142 160 180 190	392630449022
SPT(16)	2378171695310096729	0 14 18 42 50 60 110 120 182 192 242 252 260 284 288 302	537309428682
TPT(14)	2378171708336965787	0 2 24 26 114 116 162 164 204 206 234 236 252 254	550336297740
SPT(16)	2378171839958552999	0 12 44 72 102 140 174 230 294 350 384 422 452 480 512 524	681957884952
SPT(16)	2378171907746119943	0 38 44 56 78 84 108 126 128 146 170 176 198 210 216 254	749745451896