Prime p₀= 1424913147076633631 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 28 2 130 2 46 2 76 2 58 2 (?)
a_n: 0 2 18 20 48 50 180 182 228 230 306 308 366 368
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: 368
Found by: bfromcolo
db: batch=78, k=14, 16 28 130 46 76 58

STPT(10)	1424911248820148207	0 2 24 26 42 44 60 62 84 86	-1898256485424
STPT(10)	1424911526335326059	0 2 18 20 30 32 42 44 60 62	-1620741307572
SPT(16)	1424911683880576249	0 10 30 70 100 138 184 210 262 288 334 372 402 442 462 472	-1463196057382
SPT(16)	1424911790314062221	0 2 8 30 98 108 140 210 218 288 320 330 398 420 426 428	-1356762571410
SPT(18)	1424912002165856761	0 58 72 78 88 100 118 130 142 216 228 240 258 270 280 286 300 358	-1144910776870
STPT(10)	1424912425628981249	0 2 30 32 120 122 210 212 240 242	-721447652382
SPT(16)	1424913224033739061	0 40 96 142 160 180 226 250 252 276 322 342 360 406 462 502	76957105430
STPT(10)	1424913236146925477	0 2 30 32 42 44 54 56 84 86	89070291846
STPT(10)	1424913289973823281	0 2 30 32 78 80 126 128 156 158	142897189650
TPT(14)	1424913363400630307	0 2 12 14 42 44 72 74 150 152 180 182 204 206	216323996676
SPT(16)	1424913683898000469	0 12 18 82 144 172 192 294 298 400 420 448 510 574 580 592	536821366838