Prime p₀= 1245532505489272727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 52 2 64 2 58 2 22 2 46 2 (?)
a_n: 0 2 60 62 114 116 180 182 240 242 264 266 312 314
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: Cruncher Pete
db: batch=77, k=14, 58 52 64 58 22 46

STPT(10)	1245531342289334027	0 2 54 56 72 74 90 92 144 146	-1163199938700
SPT(16)	1245531453664944209	0 2 14 44 54 128 162 170 192 200 234 308 318 348 360 362	-1051824328518
STPT(10)	1245531915010388189	0 2 18 20 30 32 42 44 60 62	-590478884538
SPT(18)	1245532284294093619	0 24 82 84 120 124 148 150 154 258 262 264 288 292 328 330 388 412	-221195179108
STPT(10)	1245532320714512651	0 2 6 8 18 20 30 32 36 38	-184774760076
SPT(16)	1245532366256241779	0 2 18 20 60 114 128 144 158 174 188 242 282 284 300 302	-139233030948
TPT(14)	1245532723805768777	0 2 30 32 162 164 234 236 240 242 252 254 264 266	218316496050
SPT(16)	1245532891032776119	0 4 30 70 90 112 154 180 244 270 312 334 354 394 420 424	385543503392
TPT(14)	1245533284622603279	0 2 18 20 42 44 78 80 198 200 252 254 288 290	779133330552
SPT(16)	1245533339222262527	0 2 24 42 56 92 104 132 164 192 204 240 254 272 294 296	833732989800
SPT(16)	1245534068416120849	0 28 84 90 112 114 142 202 210 270 298 300 322 328 384 412	1562926848122