Prime p₀= 2713680066513635039 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 100 2 46 2 40 2 58 2 28 2 (?)
a_n: 0 2 18 20 120 122 168 170 210 212 270 272 300 302
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: 302
Found by: Roadranner
db: batch=82, k=14, 16 100 46 40 58 28

STPT(10)	2713678591242822809	0 2 48 50 90 92 132 134 180 182	-1475270812230
TPT(14)	2713678852846566287	0 2 72 74 114 116 174 176 180 182 210 212 222 224	-1213667068752
SPT(18)	2713679196606861341	0 8 78 110 126 140 146 218 236 342 360 432 438 452 468 500 570 578	-869906773698
SPT(16)	2713679273415279979	0 10 24 28 84 90 94 108 130 144 148 154 210 214 228 238	-793098355060
STPT(10)	2713679644763522117	0 2 42 44 72 74 102 104 144 146	-421750112922
TPT(14)	2713679871932897447	0 2 30 32 72 74 192 194 222 224 282 284 312 314	-194580737592
STPT(10)	2713680215037053699	0 2 48 50 90 92 132 134 180 182	148523418660
SPT(16)	2713680551944383011	0 6 56 78 96 110 116 146 210 240 246 260 278 300 350 356	485430747972
STPT(10)	2713680823930998587	0 2 12 14 42 44 72 74 84 86	757417363548
SPT(16)	2713680953795396257	0 66 82 100 112 124 136 154 192 210 222 234 246 264 280 346	887281761218
SPT(16)	2713681117962180001	0 60 96 142 186 250 268 298 360 390 408 472 516 562 598 658	1051448544962