Prime p₀= 2310462883353565097 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 124 2 22 2 4 2 28 2 40 2 (?)
a_n: 0 2 24 26 150 152 174 176 180 182 210 212 252 254
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: 254
Found by: FritzB
db: batch=81, k=14, 22 124 22 4 28 40

SPT(16)	2310461984878497053	0 14 18 24 80 126 134 168 206 240 248 294 350 356 360 374	-898475068044
SPT(16)	2310462047969306563	0 10 94 150 168 180 184 208 210 234 238 250 268 324 408 418	-835384258534
STPT(12)	2310462076318773437	0 2 12 14 60 62 84 86 132 134 144 146	-807034791660
SPT(16)	2310462266252532631	0 10 12 30 42 46 82 88 120 126 162 166 178 196 198 208	-617101032466
SPT(16)	2310462495814576603	0 10 54 90 106 108 114 208 276 370 376 378 394 430 474 484	-387538988494
STPT(10)	2310462550000544279	0 2 18 20 30 32 42 44 60 62	-333353020818
SPT(16)	2310462993845396111	0 18 60 66 68 78 80 122 156 198 200 210 212 218 260 278	110491831014
SPT(16)	2310463332860339047	0 10 76 94 114 124 144 202 234 292 312 322 342 360 426 436	449506773950
SPT(16)	2310463601880526879	0 24 42 54 64 78 108 112 120 124 154 168 178 190 208 232	718526961782
STPT(10)	2310463926241286087	0 2 24 26 42 44 60 62 84 86	1042887720990
SPT(16)	2310463979183372497	0 70 102 114 130 136 144 156 190 202 210 216 232 244 276 346	1095829807400