Prime p₀= 2097858175578549029 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 52 2 16 2 178 2 10 2 88 2 (?)
a_n: 0 2 18 20 72 74 90 92 270 272 282 284 372 374
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: 374
Found by: Ben
db: batch=80, k=14, 16 52 16 178 10 88

SPT(16)	2097856514258587457	0 12 14 60 90 104 134 140 306 312 342 356 386 432 434 446	-1661319961572
SPT(16)	2097856591558056227	0 26 72 86 110 120 126 140 162 176 182 192 216 230 276 302	-1584020492802
SPT(16)	2097857252387162377	0 42 52 60 72 82 94 100 126 132 144 154 166 174 184 226	-923191386652
STPT(10)	2097857730551612369	0 2 18 20 30 32 42 44 60 62	-445026936660
STPT(10)	2097857813257951091	0 2 6 8 48 50 90 92 96 98	-362320597938
TPT(14)	2097858081490334477	0 2 12 14 72 74 84 86 114 116 150 152 210 212	-94088214552
STPT(10)	2097858266836838321	0 2 6 8 48 50 90 92 96 98	91258289292
SPT(16)	2097858369450769043	0 18 44 60 84 108 128 140 174 186 206 230 254 270 296 314	193872220014
SPT(16)	2097858476089814327	0 32 42 80 96 162 182 222 224 264 284 350 366 404 414 446	300511265298
TPT(14)	2097858524598859667	0 2 12 14 72 74 84 86 192 194 210 212 240 242	349020310638
SPT(16)	2097858590620002751	0 16 36 46 52 72 76 88 90 102 106 126 132 142 162 178	415041453722