Prime p₀= 1235363986075130027 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 172 2 34 2 52 2 208 2 16 2 16 2 (?)
a_n: 0 2 174 176 210 212 264 266 474 476 492 494 510 512
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: 512
Found by: Cruncher Pete
db: batch=77, k=14, 172 34 52 208 16 16

STPT(10)	1235362782797928131	0 2 6 8 48 50 90 92 96 98	-1203277201896
SPT(16)	1235362976196019301	0 8 38 60 98 212 290 308 390 408 486 600 638 660 690 698	-1009879110726
TPT(14)	1235363166695373269	0 2 30 32 222 224 318 320 360 362 420 422 450 452	-819379756758
STPT(10)	1235363382181543787	0 2 12 14 72 74 132 134 144 146	-603893586240
STPT(10)	1235363491895243531	0 2 6 8 18 20 30 32 36 38	-494179886496
SPT(16)	1235363848678873169	0 60 72 114 170 224 240 242 312 314 330 384 440 482 494 554	-137396256858
SPT(16)	1235364340287709127	0 56 72 156 192 210 236 290 312 366 392 410 446 530 546 602	354212579100
SPT(16)	1235364776429670067	0 16 46 96 112 124 150 192 214 256 282 294 310 360 390 406	790354540040
TPT(14)	1235365118712940541	0 2 30 32 126 128 186 188 228 230 240 242 258 260	1132637810514
STPT(10)	1235365232481351869	0 2 42 44 60 62 78 80 120 122	1246406221842
SPT(16)	1235365310933031589	0 10 100 112 132 150 160 204 238 282 292 310 330 342 432 442	1324857901562