Prime p₀= 4044828849140192159 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 34 2 10 2 70 2 4 2 28 2 (?)
a_n: 0 2 12 14 48 50 60 62 132 134 138 140 168 170
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: 170
Found by: Alnitak2019
db: batch=84, k=14, 10 34 10 70 4 28

SPT(16)	4044828126921112673	0 6 18 86 90 116 140 156 158 174 198 224 228 296 308 314	-722219079486
STPT(10)	4044828163529172989	0 2 12 14 30 32 48 50 60 62	-685611019170
SPT(16)	4044828333604944091	0 16 40 82 108 118 120 150 208 238 240 250 276 318 342 358	-515535248068
SPT(16)	4044828344177067649	0 12 82 88 90 112 138 222 250 334 360 382 384 390 460 472	-504963124510
TPT(14)	4044828756832784717	0 2 240 242 252 254 474 476 480 482 522 524 564 566	-92307407442
STPT(10)	4044828780312926729	0 2 12 14 30 32 48 50 60 62	-68827265430
STPT(12)	4044829111017687359	0 2 12 14 42 44 78 80 108 110 120 122	261877495200
STPT(10)	4044829155941387237	0 2 54 56 72 74 90 92 144 146	306801195078
STPT(10)	4044829685182875599	0 2 48 50 90 92 132 134 180 182	836042683440
SPT(16)	4044831002488480951	0 10 48 96 102 136 178 222 286 330 372 406 412 460 498 508	2153348288792
TPT(14)	4044831315936710417	0 2 54 56 72 74 180 182 240 242 252 254 264 266	2466796518258