Prime p₀= 316751144373468359 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 10 2 70 2 76 2 16 2 (?)
a_n: 0 2 78 80 90 92 162 164 240 242 258 260
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: 260
Found by: desktop64
db: batch=70, k=12, 76 10 70 76 16

SPT(14)	316751097622279289	0 2 48 50 72 78 84 98 104 110 132 134 180 182	-46751189070
SPT(14)	316751099650989779	0 20 24 32 74 90 102 152 164 180 222 230 234 254	-44722478580
SPT(14)	316751100127384141	0 10 16 30 36 60 120 136 196 220 226 240 246 256	-44246084218
SPT(14)	316751114814248573	0 50 60 68 78 90 114 200 224 236 246 254 264 314	-29559219786
STPT(10)	316751121548390729	0 2 48 50 90 92 132 134 180 182	-22825077630
TPT(14)	316751141438452991	0 2 48 50 90 92 270 272 396 398 468 470 480 482	-2935015368
SPT(16)	316751153831049701	0 12 80 110 128 180 192 200 318 326 338 390 408 438 506 518	9457581342
SPT(14)	316751158795272073	0 4 28 36 46 90 96 118 124 168 178 186 210 214	14421803714
TPT(12)	316751166370917041	0 2 30 32 96 98 240 242 366 368 450 452	21997448682
SPT(14)	316751179046572733	0 14 84 140 150 168 170 234 236 254 264 320 390 404	34673104374
SPT(14)	316751204367476521	0 48 60 82 112 196 222 286 312 396 426 448 460 508	59994008162