Prime p₀= 1245533284622603279 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 34 2 118 2 52 2 34 2 (?)
a_n: 0 2 18 20 42 44 78 80 198 200 252 254 288 290
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: 290
Found by: Cruncher Pete
db: batch=77, k=14, 16 22 34 118 52 34

SPT(18)	1245532284294093619	0 24 82 84 120 124 148 150 154 258 262 264 288 292 328 330 388 412	-1000328509660
STPT(10)	1245532320714512651	0 2 6 8 18 20 30 32 36 38	-963908090628
SPT(16)	1245532366256241779	0 2 18 20 60 114 128 144 158 174 188 242 282 284 300 302	-918366361500
TPT(14)	1245532505489272727	0 2 60 62 114 116 180 182 240 242 264 266 312 314	-779133330552
TPT(14)	1245532723805768777	0 2 30 32 162 164 234 236 240 242 252 254 264 266	-560816834502
SPT(16)	1245532891032776119	0 4 30 70 90 112 154 180 244 270 312 334 354 394 420 424	-393589827160
SPT(16)	1245533339222262527	0 2 24 42 56 92 104 132 164 192 204 240 254 272 294 296	54599659248
SPT(16)	1245534068416120849	0 28 84 90 112 114 142 202 210 270 298 300 322 328 384 412	783793517570
STPT(10)	1245534199503915941	0 2 6 8 48 50 90 92 96 98	914881312662
SPT(16)	1245534620459405293	0 6 24 138 154 160 168 216 238 286 294 300 316 430 448 454	1335836802014
SPT(16)	1245535031232186329	0 12 18 60 98 108 150 228 284 362 404 414 452 494 500 512	1746609583050