Prime p₀= 2731860788689128749 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 10 2 58 2 46 2 16 2 10 2 (?)
a_n: 0 2 90 92 102 104 162 164 210 212 228 230 240 242
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: 242
Found by: Coleslaw
db: batch=82, k=14, 88 10 58 46 16 10

STPT(10)	2731859550350654567	0 2 30 32 42 44 54 56 84 86	-1238338474182
TPT(14)	2731859961939103781	0 2 36 38 60 62 156 158 186 188 216 218 240 242	-826750024968
SPT(16)	2731860020734886183	0 44 80 90 128 140 198 206 258 266 324 336 374 384 420 464	-767954242566
STPT(10)	2731860164868225437	0 2 12 14 72 74 132 134 144 146	-623820903312
SPT(16)	2731860389796894409	0 4 40 48 118 130 154 202 210 258 282 294 364 372 408 412	-398892234340
SPT(16)	2731860756925458203	0 6 14 36 50 80 138 146 198 206 264 294 308 330 338 344	-31763670546
SPT(16)	2731860950134375859	0 20 42 62 72 98 114 132 140 158 174 200 210 230 252 272	161445247110
STPT(10)	2731861018470804677	0 2 30 32 72 74 114 116 144 146	229781675928
SPT(16)	2731861028904488659	0 24 34 70 72 84 184 244 258 318 418 430 432 468 478 502	240215359910
SPT(16)	2731861290195400619	0 2 44 72 90 92 152 168 224 240 300 302 320 348 390 392	501506271870
TPT(14)	2731861400604809321	0 2 60 62 90 92 396 398 408 410 450 452 456 458	611915680572