Prime p₀= 1323150873848528189 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 166 2 10 2 10 2 16 2 118 2 40 2 (?)
a_n: 0 2 168 170 180 182 192 194 210 212 330 332 372 374
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 374
Found by: Megacruncher
db: batch=77, k=14, 166 10 10 16 118 40

SPT(16)	1323148769445799409	0 14 50 54 80 84 98 150 182 234 248 252 278 282 318 332	-2104402728780
STPT(10)	1323148781335019459	0 2 18 20 30 32 42 44 60 62	-2092513508730
SPT(16)	1323148872388390393	0 10 30 40 66 78 106 120 154 168 196 208 234 244 264 274	-2001460137796
SPT(16)	1323149925997511881	0 10 16 66 96 136 166 180 196 210 240 280 310 360 366 376	-947851016308
SPT(16)	1323150249067640221	0 16 42 78 82 106 112 118 120 126 132 156 160 196 222 238	-624780887968
SPT(20)	1323150767847945739	0 10 22 24 28 58 72 108 148 154 288 294 334 370 384 414 418 420 432 442	-106000582450
SPT(16)	1323151084462721957	0 62 72 80 102 176 216 282 344 410 450 524 546 554 564 626	210614193768
STPT(10)	1323151188445423619	0 2 18 20 60 62 102 104 120 122	314596895430
STPT(10)	1323151543119401531	0 2 6 8 48 50 90 92 96 98	669270873342
STPT(10)	1323151590739687727	0 2 12 14 72 74 132 134 144 146	716891159538
STPT(10)	1323151746951086747	0 2 30 32 60 62 90 92 120 122	873102558558