Prime p₀= 2027560690221021869 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 70 2 136 2 70 2 34 2 (?)
a_n: 0 2 42 44 60 62 132 134 270 272 342 344 378 380
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: 380
Found by: Orange Kid
db: batch=80, k=14, 40 16 70 136 70 34

STPT(10)	2027559266085756827	0 2 54 56 72 74 90 92 144 146	-1424135265042
SPT(16)	2027559326730502093	0 28 88 118 144 168 184 210 244 270 286 310 336 366 426 454	-1363490519776
STPT(10)	2027559442100097077	0 2 30 32 42 44 54 56 84 86	-1248120924792
STPT(10)	2027559487984885469	0 2 18 20 30 32 42 44 60 62	-1202236136400
TPT(14)	2027559879236901941	0 2 66 68 96 98 120 122 138 140 150 152 156 158	-810984119928
STPT(10)	2027560514967819437	0 2 12 14 72 74 132 134 144 146	-175253202432
SPT(16)	2027560694682263863	0 40 78 94 96 148 150 174 280 304 306 358 360 376 414 454	4461241994
SPT(16)	2027560896639059791	0 16 28 70 88 100 130 132 196 198 228 240 258 300 312 328	206418037922
SPT(16)	2027561057124202837	0 30 34 70 72 180 184 196 240 252 256 364 366 402 406 436	366903180968
SPT(16)	2027561093026245331	0 60 90 102 178 210 228 252 286 310 328 360 436 448 478 538	402805223462
TPT(14)	2027561274319400549	0 2 90 92 168 170 312 314 342 344 372 374 408 410	584098378680