Prime p₀= 2928725475598783697 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 70 2 64 2 28 2 10 2 88 2 (?)
a_n: 0 2 42 44 114 116 180 182 210 212 222 224 312 314
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: 314
Found by: Landjunge
db: batch=82, k=14, 40 70 64 28 10 88

SPT(16)	2928723104595959087	0 2 30 60 104 114 126 140 216 230 242 252 296 326 354 356	-2371002824610
SPT(16)	2928723760681704121	0 12 70 76 78 82 120 138 190 208 246 250 252 258 316 328	-1714917079576
SPT(16)	2928723838492998289	0 34 184 204 214 240 280 358 420 498 538 564 574 594 744 778	-1637105785408
TPT(14)	2928723850942608317	0 2 132 134 222 224 282 284 420 422 432 434 474 476	-1624656175380
SPT(16)	2928724774330558261	0 42 76 130 168 172 178 192 196 210 216 220 258 312 346 388	-701268225436
SPT(16)	2928725296565826937	0 22 34 60 64 82 90 154 180 244 252 270 274 300 312 334	-179032956760
STPT(10)	2928725499512514599	0 2 18 20 60 62 102 104 120 122	23913730902
STPT(10)	2928725513930567381	0 2 30 32 60 62 90 92 120 122	38331783684
STPT(10)	2928725616104235989	0 2 18 20 30 32 42 44 60 62	140505452292
SPT(16)	2928725618216458393	0 34 36 40 76 84 90 120 124 154 160 168 204 208 210 244	142617674696
TPT(14)	2928725959419495197	0 2 30 32 72 74 144 146 174 176 180 182 210 212	483820711500