Prime p₀= 2642662728091364399 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 28 2 40 2 28 2 10 2 58 2 (?)
a_n: 0 2 78 80 108 110 150 152 180 182 192 194 252 254
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: [SG-FC] hl
db: batch=82, k=14, 76 28 40 28 10 58

SPT(16)	2642661204529787899	0 54 58 100 118 160 204 210 232 238 282 324 342 384 388 442	-1523561576500
STPT(10)	2642661293421815789	0 2 12 14 30 32 48 50 60 62	-1434669548610
STPT(10)	2642661604286032751	0 2 36 38 78 80 120 122 156 158	-1123805331648
SPT(16)	2642662159590232489	0 12 28 58 72 84 112 154 168 210 238 250 264 294 310 322	-568501131910
STPT(10)	2642662560905560001	0 2 6 8 48 50 90 92 96 98	-167185804398
SPT(16)	2642662639733287333	0 16 78 84 100 156 184 186 208 210 238 294 310 316 378 394	-88358077066
TPT(14)	2642662774885540409	0 2 120 122 132 134 168 170 210 212 270 272 300 302	46794176010
SPT(16)	2642662927961524999	0 58 60 72 114 208 244 264 328 348 384 478 520 532 534 592	199870160600
STPT(10)	2642663036746168529	0 2 18 20 30 32 42 44 60 62	308654804130
SPT(16)	2642663348091724831	0 16 40 52 82 102 108 112 126 130 136 156 186 198 222 238	620000360432
SPT(16)	2642663481074537309	0 78 110 152 158 198 242 308 342 408 452 492 498 540 572 650	752983172910