Prime p₀= 2568351686708629067 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 46 2 40 2 118 2 4 2 10 2 (?)
a_n: 0 2 24 26 72 74 114 116 234 236 240 242 252 254
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: RFGuy_KCCO
db: batch=82, k=14, 22 46 40 118 4 10

SPT(16)	2568350958357468959	0 12 48 50 114 188 192 240 272 320 324 398 462 464 500 512	-728351160108
STPT(10)	2568350972156317847	0 2 30 32 72 74 114 116 144 146	-714552311220
SPT(16)	2568350975755409149	0 34 78 82 118 132 138 144 148 154 160 174 210 214 258 292	-710953219918
SPT(16)	2568351361438303783	0 4 46 70 130 168 174 184 210 220 226 264 324 348 390 394	-325270325284
SPT(16)	2568351431772123511	0 28 52 90 96 112 120 178 180 238 246 262 268 306 330 358	-254936505556
SPT(16)	2568351474044098993	0 34 40 66 70 94 150 196 228 274 330 354 358 384 390 424	-212664530074
SPT(16)	2568351719495620733	0 30 56 78 96 108 110 156 218 264 266 278 296 318 344 374	32786991666
STPT(10)	2568352224812874551	0 2 6 8 18 20 30 32 36 38	538104245484
TPT(14)	2568352426738187849	0 2 42 44 138 140 168 170 240 242 258 260 438 440	740029558782
SPT(13)	2568352606586855411	0 36 42 60 72 126 156 186 240 252 270 276 312	919878226344
SPT(16)	2568352717660615909	0 22 24 48 88 112 114 118 144 148 150 174 214 238 240 262	1030951986842