Prime p₀= 2387557789971076277 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 130 2 64 2 40 2 16 2 22 2 (?)
a_n: 0 2 42 44 174 176 240 242 282 284 300 302 324 326
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: Landjunge
db: batch=81, k=14, 40 130 64 40 16 22

TPT(14)	2387556686778343037	0 2 24 26 72 74 114 116 144 146 180 182 222 224	-1103192733240
SPT(16)	2387557012701845177	0 6 32 42 50 90 96 116 156 176 182 222 230 240 266 272	-777269231100
SPT(16)	2387557166244463861	0 30 48 126 160 186 222 226 282 286 322 348 382 460 478 508	-623726612416
STPT(12)	2387557312182257909	0 2 42 44 72 74 78 80 108 110 150 152	-477788818368
STPT(10)	2387557385263099961	0 2 6 8 18 20 30 32 36 38	-404707976316
STPT(10)	2387557621290799187	0 2 24 26 42 44 60 62 84 86	-168680277090
SPT(16)	2387558817634825379	0 2 12 18 72 74 80 84 128 132 138 140 194 200 210 212	1027663749102
SPT(16)	2387560292787198989	0 48 104 140 180 204 210 218 264 272 278 302 342 378 434 482	2502816122712
SPT(16)	2387560456984242979	0 28 48 60 82 108 112 124 138 150 154 180 202 214 234 262	2667013166702
STPT(10)	2387560539842699027	0 2 42 44 72 74 102 104 144 146	2749871622750
STPT(10)	2387560939959719219	0 2 12 14 90 92 168 170 180 182	3149988642942