Prime p₀= 2502397189339465967 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 40 2 4 2 40 2 40 2 (?)
a_n: 0 2 42 44 84 86 90 92 132 134 174 176
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: 176
Found by: Penguin
db: batch=82, k=12, 2 40 2 40 2 4

SPT(16)	2502394973222519821	0 6 52 76 120 130 150 160 222 232 252 262 306 330 376 382	-2216116946146
SPT(16)	2502396346831014509	0 14 38 68 74 102 120 140 162 182 200 228 234 264 288 302	-842508451458
STPT(12)	2502396404688979739	0 2 12 14 42 44 48 50 78 80 90 92	-784650486228
TPT(14)	2502396443686618097	0 2 54 56 84 86 90 92 132 134 372 374 390 392	-745652847870
STPT(10)	2502396639597663629	0 2 42 44 60 62 78 80 120 122	-549741802338
SPT(16)	2502397158216106457	0 20 54 60 66 96 116 144 146 174 194 224 230 236 270 290	-31123359510
STPT(10)	2502397473802900097	0 2 30 32 72 74 114 116 144 146	284463434130
STPT(10)	2502397646625387629	0 2 18 20 30 32 42 44 60 62	457285921662
SPT(16)	2502397767603937327	0 34 42 46 70 90 112 180 196 264 286 306 330 334 342 376	578264471360
SPT(16)	2502398296819257563	0 6 18 44 48 74 104 128 156 180 210 236 240 266 278 284	1107479791596
STPT(10)	2502398419247002217	0 2 30 32 42 44 54 56 84 86	1229907536250