Prime p₀= 2134481579566699667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 130 2 16 2 10 2 58 2 34 2 (?)
a_n: 0 2 42 44 174 176 192 194 204 206 264 266 300 302
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: 302
Found by: Coleslaw
db: batch=80, k=14, 40 130 16 10 58 34

STPT(10)	2134480253255781749	0 2 42 44 90 92 138 140 180 182	-1326310917918
SPT(16)	2134480546603562137	0 10 24 30 84 106 142 166 210 234 270 292 346 352 366 376	-1032963137530
SPT(16)	2134480602779652007	0 46 52 102 124 130 132 150 196 214 216 222 244 294 300 346	-976787047660
STPT(10)	2134480930474071167	0 2 30 32 102 104 174 176 204 206	-649092628500
SPT(16)	2134481291593647119	0 54 78 90 114 128 168 194 198 224 264 278 302 314 338 392	-287973052548
SPT(16)	2134481340151636219	0 22 84 132 142 148 210 232 240 262 324 330 340 388 450 472	-239415063448
STPT(10)	2134481696797917107	0 2 84 86 132 134 180 182 264 266	117231217440
SPT(16)	2134481777096152189	0 28 40 54 70 94 138 154 264 280 324 348 364 378 390 418	197529452522
SPT(16)	2134482054483932557	0 4 46 52 54 130 154 162 304 312 336 412 414 420 462 466	474917232890
SPT(16)	2134482290128097809	0 30 54 60 64 70 78 100 102 124 132 138 142 148 172 202	710561398142
SPT(16)	2134482663852979729	0 28 48 60 70 154 172 178 234 240 258 342 352 364 384 412	1084286280062