Prime p₀= 1042321879556944871 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 28 2 28 2 148 2 22 2 58 2 (?)
a_n: 0 2 66 68 96 98 126 128 276 278 300 302 360 362
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: 362
Found by: stoneageman
db: batch=76, k=14, 64 28 28 148 22 58

SPT(16)	1042319470839844807	0 12 16 54 96 100 166 186 190 210 276 280 322 360 364 376	-2408717100064
STPT(10)	1042319929443028667	0 2 12 14 72 74 132 134 144 146	-1950113916204
STPT(10)	1042320036478930787	0 2 30 32 42 44 54 56 84 86	-1843078014084
SPT(16)	1042320675950811227	0 12 42 80 102 116 144 150 176 182 210 224 246 284 314 326	-1203606133644
SPT(16)	1042321354110006559	0 10 30 70 108 120 144 208 210 274 298 310 348 388 408 418	-525446938312
SPT(16)	1042321473864888953	0 14 66 80 116 140 164 170 234 240 264 288 324 338 390 404	-405692055918
STPT(10)	1042321914768787097	0 2 54 56 132 134 210 212 264 266	35211842226
SPT(16)	1042322089053564841	0 42 90 106 120 132 156 162 166 172 196 208 222 238 286 328	209496619970
SPT(16)	1042322128622014393	0 4 24 46 70 84 114 126 184 196 226 240 264 286 306 310	249065069522
TPT(14)	1042322290086105827	0 2 12 14 30 32 42 44 162 164 204 206 234 236	410529160956
STPT(10)	1042322577155361389	0 2 18 20 30 32 42 44 60 62	697598416518