Prime p₀= 2031135639262694957 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 58 2 64 2 10 2 88 2 40 2 (?)
a_n: 0 2 54 56 114 116 180 182 192 194 282 284 324 326
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: 326
Found by: Dingo
db: batch=80, k=14, 52 58 64 10 88 40

STPT(10)	2031133455743152301	0 2 30 32 78 80 126 128 156 158	-2183519542656
TPT(14)	2031134122386918929	0 2 42 44 48 50 72 74 78 80 252 254 282 284	-1516875776028
STPT(12)	2031134159831836649	0 2 18 20 42 44 78 80 102 104 120 122	-1479430858308
SPT(16)	2031134240213394919	0 4 40 78 82 142 168 172 180 184 210 270 274 312 348 352	-1399049300038
SPT(16)	2031134300797284391	0 16 48 76 172 190 238 288 310 360 408 426 522 550 582 598	-1338465410566
SPT(16)	2031135251114324881	0 16 22 42 52 58 60 100 198 238 240 246 256 276 282 298	-388148370076
SPT(16)	2031136209983144521	0 48 70 112 148 162 186 202 306 322 346 360 396 438 460 508	570720449564
STPT(10)	2031136571328373307	0 2 30 32 42 44 54 56 84 86	932065678350
SPT(16)	2031136666313487637	0 34 60 64 76 114 160 186 214 240 286 324 336 340 366 400	1027050792680
SPT(16)	2031136667828544943	0 16 30 46 130 156 184 234 280 330 358 384 468 484 498 514	1028565849986
SPT(13)	2031136802549647477	0 24 66 90 126 144 150 156 174 210 234 276 300	1163286952520