Prime p₀= 2157306161985989627 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 88 2 46 2 28 2 10 2 4 2 (?)
a_n: 0 2 84 86 174 176 222 224 252 254 264 266 270 272
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: 272
Found by: Landjunge
db: batch=81, k=14, 82 88 46 28 10 4

SPT(16)	2157305512890975169	0 4 48 60 78 88 114 118 240 244 270 280 298 310 354 358	-649095014458
SPT(16)	2157305516073445369	0 10 120 154 172 192 214 240 274 300 322 342 360 394 504 514	-645912544258
SPT(16)	2157305739459476059	0 4 10 70 82 88 124 150 172 198 234 240 252 312 318 322	-422526513568
SPT(16)	2157305924516316017	0 12 42 72 122 134 146 164 222 240 252 264 314 344 374 386	-237469673610
TPT(14)	2157306057877216031	0 2 36 38 78 80 90 92 126 128 156 158 168 170	-104108773596
SPT(16)	2157306131875374031	0 52 76 112 118 142 168 222 256 310 336 360 366 402 426 478	-30110615596
STPT(10)	2157306401894293547	0 2 42 44 72 74 102 104 144 146	239908303920
STPT(10)	2157306498092664377	0 2 30 32 42 44 54 56 84 86	336106674750
STPT(10)	2157306700714310441	0 2 6 8 18 20 30 32 36 38	538728320814
SPT(16)	2157307336182470819	0 32 50 54 74 78 84 128 144 188 194 198 218 222 240 272	1174196481192
STPT(10)	2157307430299184921	0 2 6 8 18 20 30 32 36 38	1268313195294