Prime p₀= 2062931862733679141 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 16 2 148 2 58 2 10 2 16 2 (?)
a_n: 0 2 78 80 96 98 246 248 306 308 318 320 336 338
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: 338
Found by: Cruncher Pete
db: batch=80, k=14, 76 16 148 58 10 16

SPT(16)	2062930383658914551	0 12 18 38 42 56 80 90 278 288 312 326 330 350 356 368	-1479074764590
STPT(10)	2062930605084360281	0 2 6 8 48 50 90 92 96 98	-1257649318860
STPT(10)	2062930634962506107	0 2 30 32 120 122 210 212 240 242	-1227771173034
SPT(16)	2062930982284609543	0 10 18 40 78 88 108 126 190 208 228 238 276 298 306 316	-880449069598
TPT(14)	2062931269253886209	0 2 12 14 78 80 162 164 222 224 330 332 462 464	-593479792932
STPT(10)	2062931530944600101	0 2 30 32 78 80 126 128 156 158	-331789079040
SPT(16)	2062932064833064511	0 20 30 38 56 66 78 116 132 170 182 192 210 218 228 248	202099385370
SPT(16)	2062932065632577521	0 18 42 70 82 100 166 196 312 342 408 426 438 466 490 508	202898898380
SPT(16)	2062932271122438907	0 10 24 42 66 102 114 120 136 142 154 190 214 232 246 256	408388759766
SPT(16)	2062932627786993077	0 12 26 62 90 92 96 140 216 260 264 266 294 330 344 356	765053313936
STPT(10)	2062932879628987151	0 2 36 38 78 80 120 122 156 158	1016895308010