Prime p₀= 2354953723294223627 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 88 2 10 2 16 2 10 2 94 2 (?)
a_n: 0 2 42 44 132 134 144 146 162 164 174 176 270 272
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, 40 88 10 16 10 94

SPT(16)	2354952030300176063	0 54 78 80 150 164 168 180 224 236 240 254 324 326 350 404	-1692994047564
SPT(16)	2354952625675431373	0 4 18 40 70 114 118 138 160 180 184 228 258 280 294 298	-1097618792254
STPT(10)	2354952847843272959	0 2 42 44 60 62 78 80 120 122	-875450950668
SPT(16)	2354953176788813311	0 22 40 96 100 112 168 190 258 280 336 348 352 408 426 448	-546505410316
SPT(16)	2354953647393968147	0 2 66 80 102 126 170 186 230 246 290 314 336 350 414 416	-75900255480
SPT(16)	2354953654288648603	0 36 64 88 94 120 144 166 168 190 214 240 246 270 298 334	-69005575024
SPT(16)	2354953889672881537	0 10 22 52 102 106 126 190 192 256 276 280 330 360 372 382	166378657910
STPT(10)	2354954100090466541	0 2 6 8 18 20 30 32 36 38	376796242914
STPT(10)	2354954342381911607	0 2 30 32 42 44 54 56 84 86	619087687980
SPT(16)	2354954604571537637	0 6 30 32 84 110 114 116 210 212 216 242 294 296 320 326	881277314010
TPT(14)	2354954917992885641	0 2 66 68 96 98 156 158 168 170 186 188 198 200	1194698662014