Prime p₀= 2095457510856914117 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 22 2 148 2 4 2 28 2 (?)
a_n: 0 2 60 62 90 92 114 116 264 266 270 272 300 302
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: Landjunge
db: batch=80, k=14, 58 28 22 148 4 28

SPT(16)	2095456405367914931	0 2 42 96 102 140 146 156 212 222 228 266 272 326 366 368	-1105488999186
SPT(16)	2095456574987189969	0 8 14 38 74 144 168 170 282 284 308 378 414 438 444 452	-935869724148
SPT(16)	2095456680017729227	0 12 16 40 70 90 114 156 160 202 226 246 276 300 304 316	-830839184890
STPT(10)	2095456808929653509	0 2 18 20 30 32 42 44 60 62	-701927260608
SPT(16)	2095456839602146309	0 24 48 84 130 144 150 174 238 262 268 282 328 364 388 412	-671254767808
STPT(10)	2095456871708870741	0 2 30 32 78 80 126 128 156 158	-639148043376
STPT(10)	2095457673745388549	0 2 42 44 60 62 78 80 120 122	162888474432
SPT(16)	2095457732572894093	0 6 76 84 96 144 180 186 244 250 286 334 346 354 424 430	221715979976
SPT(16)	2095457820193449479	0 78 108 188 218 224 242 290 312 360 378 384 414 494 524 602	309336535362
SPT(16)	2095457851392380177	0 30 50 104 110 120 140 164 180 204 224 234 240 294 314 344	340535466060
TPT(14)	2095458213858265301	0 2 36 38 48 50 78 80 90 92 108 110 138 140	703001351184