Prime p₀= 1268979723951983999 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 208 2 136 2 22 2 46 2 (?)
a_n: 0 2 60 62 90 92 300 302 438 440 462 464 510 512
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: 512
Found by: mikey
db: batch=77, k=14, 58 28 208 136 22 46

SPT(16)	1268979041779329233	0 30 68 80 114 126 140 156 218 234 248 260 294 306 344 374	-682172654766
STPT(10)	1268979072704253899	0 2 18 20 30 32 42 44 60 62	-651247730100
SPT(16)	1268979194157717971	0 8 42 78 96 122 168 180 188 200 246 272 290 326 360 368	-529794266028
SPT(16)	1268979194734266293	0 36 146 150 210 218 258 260 306 308 348 356 416 420 530 566	-529217717706
STPT(10)	1268979243606177911	0 2 90 92 150 152 210 212 300 302	-480345806088
STPT(10)	1268979409677907391	0 2 36 38 78 80 120 122 156 158	-314274076608
SPT(16)	1268980170443598199	0 10 28 30 34 52 72 130 222 280 300 318 322 324 342 352	446491614200
SPT(16)	1268980215698833081	0 6 28 30 48 58 66 70 96 100 108 118 136 138 160 166	491746849082
SPT(16)	1268980313555398109	0 24 44 84 108 120 134 180 182 228 242 254 278 318 338 362	589603414110
SPT(18)	1268980637705979283	0 16 30 40 46 64 100 166 196 198 228 294 330 348 354 364 378 394	913753995284
SPT(16)	1268980737384384259	0 4 28 72 144 162 184 198 214 228 250 268 340 384 408 412	1013432400260