Prime p₀= 2316496160929276871 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 40 2 34 2 22 2 94 2 28 2 (?)
a_n: 0 2 108 110 150 152 186 188 210 212 306 308 336 338
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: 338
Found by: Landjunge
db: batch=81, k=14, 106 40 34 22 94 28

STPT(10)	2316495384312155729	0 2 42 44 90 92 138 140 180 182	-776617121142
SPT(16)	2316495503743017593	0 6 36 66 84 138 140 150 164 174 176 230 248 278 308 314	-657186259278
STPT(10)	2316495566421407981	0 2 30 32 78 80 126 128 156 158	-594507868890
TPT(14)	2316495824636053547	0 2 60 62 90 92 222 224 282 284 300 302 312 314	-336293223324
SPT(16)	2316495914028162899	0 32 42 50 74 92 120 152 162 194 222 240 264 272 282 314	-246901113972
SPT(16)	2316496151926129181	0 66 72 126 150 162 182 218 240 276 296 308 332 386 392 458	-9003147690
SPT(16)	2316496525814782231	0 42 60 126 142 162 180 196 216 232 250 270 286 352 370 412	364885505360
SPT(16)	2316496647861451243	0 6 88 100 156 160 196 216 238 258 294 298 354 366 448 454	486932174372
STPT(10)	2316496652156471969	0 2 18 20 30 32 42 44 60 62	491227195098
SPT(18)	2316496989697804217	0 2 44 54 72 162 182 264 282 314 332 414 434 524 542 552 594 596	828768527346
TPT(14)	2316497239669903097	0 2 42 44 84 86 90 92 162 164 174 176 264 266	1078740626226