Prime p₀= 2261421072273101279 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 58 2 28 2 64 2 70 2 40 2 (?)
a_n: 0 2 72 74 132 134 162 164 228 230 300 302 342 344
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: 344
Found by: MarkRBright
db: batch=81, k=14, 70 58 28 64 70 40

SPT(16)	2261417710688957473	0 34 58 60 64 70 160 190 198 228 318 324 328 330 354 388	-3361584143806
STPT(10)	2261418096894756599	0 2 48 50 60 62 72 74 120 122	-2975378344680
STPT(10)	2261418385804477577	0 2 30 32 42 44 54 56 84 86	-2686468623702
STPT(10)	2261419643936963747	0 2 12 14 42 44 72 74 84 86	-1428336137532
STPT(10)	2261419982915472719	0 2 18 20 30 32 42 44 60 62	-1089357628560
TPT(16)	2261420143520733047	0 2 30 32 54 56 84 86 114 116 144 146 282 284 312 314	-928752368232
STPT(10)	2261421083976428147	0 2 12 14 72 74 132 134 144 146	11703326868
TPT(14)	2261421486310255739	0 2 30 32 120 122 138 140 162 164 222 224 240 242	414037154460
SPT(18)	2261421513863985197	0 44 50 74 92 96 114 140 174 182 216 242 260 264 282 306 312 356	441590883918
STPT(10)	2261421744764512787	0 2 30 32 72 74 114 116 144 146	672491411508
SPT(18)	2261421870807932471	0 8 188 216 270 276 290 302 326 342 366 378 392 398 452 480 660 668	798534831192