Prime p₀= 2960418755329870337 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 10 2 28 2 76 2 28 2 28 2 (?)
a_n: 0 2 72 74 84 86 114 116 192 194 222 224 252 254
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: 254
Found by: Landjunge
db: batch=82, k=14, 70 10 28 76 28 28

SPT(16)	2960417398528605091	0 10 18 42 82 118 156 168 310 322 360 396 436 460 468 478	-1356801265246
SPT(16)	2960417848369451299	0 30 60 78 112 114 174 198 244 268 328 330 364 382 412 442	-906960419038
SPT(16)	2960417957204557583	0 6 24 38 44 90 140 156 158 174 224 270 276 290 308 314	-798125312754
STPT(10)	2960418019261660169	0 2 18 20 60 62 102 104 120 122	-736068210168
STPT(10)	2960418053596500527	0 2 30 32 60 62 90 92 120 122	-701733369810
STPT(10)	2960418163777575869	0 2 18 20 30 32 42 44 60 62	-591552294468
SPT(16)	2960418768046321207	0 6 10 40 112 202 216 220 222 226 240 330 402 432 436 442	12716450870
STPT(10)	2960418948056715989	0 2 18 20 30 32 42 44 60 62	192726845652
SPT(16)	2960419093126606327	0 34 72 76 84 142 154 192 244 282 294 352 360 364 402 436	337796735990
SPT(16)	2960419155448693877	0 42 86 92 102 116 180 182 240 242 306 320 330 336 380 422	400118823540
TPT(14)	2960419398126643331	0 2 48 50 60 62 90 92 126 128 156 158 168 170	642796772994