Prime p₀= 1245750648728049551 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 58 2 22 2 46 2 10 2 94 2 (?)
a_n: 0 2 6 8 66 68 90 92 138 140 150 152 246 248
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: 248
Found by: Cruncher Pete
db: batch=77, k=14, 4 58 22 46 10 94

STPT(10)	1245748604224653101	0 2 126 128 138 140 150 152 276 278	-2044503396450
SPT(16)	1245749079245332913	0 56 66 104 146 150 180 194 210 224 254 258 300 338 348 404	-1569482716638
STPT(10)	1245749449542903671	0 2 36 38 78 80 120 122 156 158	-1199185145880
STPT(10)	1245749582755089857	0 2 30 32 42 44 54 56 84 86	-1065972959694
SPT(16)	1245749654211233533	0 24 40 48 64 66 96 108 136 148 178 180 196 204 220 244	-994516816018
TPT(14)	1245749678489448071	0 2 30 32 186 188 198 200 216 218 408 410 450 452	-970238601480
STPT(10)	1245751305748397417	0 2 54 56 72 74 90 92 144 146	657020347866
SPT(16)	1245751348635763793	0 18 38 50 80 104 116 134 150 168 180 204 234 246 266 284	699907714242
SPT(16)	1245751452514695421	0 22 58 72 120 142 148 150 190 192 198 220 268 282 318 340	803786645870
SPT(16)	1245751780207871009	0 20 62 68 78 80 98 110 120 132 150 152 162 168 210 230	1131479821458
SPT(16)	1245751814825207509	0 4 24 30 42 70 88 172 210 294 312 340 352 358 378 382	1166097157958