Prime p₀= 1427257816612034051 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 30 32 66 68 78 80 108 110 138 140 150 152
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: 152
Found by: MarkRBright
db: batch=78, k=14, 28 34 10 28 28 10

STPT(10)	1427255540873261789	0 2 18 20 30 32 42 44 60 62	-2275738772262
SPT(18)	1427255601133019429	0 72 78 102 134 140 258 312 314 408 410 464 582 588 620 644 650 722	-2215479014622
STPT(10)	1427256242273640377	0 2 30 32 42 44 54 56 84 86	-1574338393674
SPT(16)	1427256630920642647	0 6 10 72 112 156 192 202 210 220 256 300 340 402 406 412	-1185691391404
SPT(16)	1427257141086946493	0 36 134 158 210 216 246 258 296 308 338 344 396 420 518 554	-675525087558
SPT(16)	1427257474567568351	0 2 8 38 78 102 192 218 312 338 428 452 492 522 528 530	-342044465700
STPT(10)	1427257816612034117	0 2 12 14 42 44 72 74 84 86	66
SPT(16)	1427258194744818767	0 2 62 92 104 114 192 240 266 314 392 402 414 444 504 506	378132784716
STPT(10)	1427258228576810207	0 2 30 32 42 44 54 56 84 86	411964776156
SPT(16)	1427258319699663749	0 8 42 68 72 102 162 200 240 278 338 368 372 398 432 440	503087629698
SPT(16)	1427258368381869833	0 18 50 78 84 110 120 134 150 164 174 200 206 234 266 284	551769835782