Prime p₀= 1299488823431000261 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 100 2 106 2 10 2 124 2 58 2 (?)
a_n: 0 2 78 80 180 182 288 290 300 302 426 428 486 488
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: 488
Found by: Theadalus
db: batch=77, k=14, 76 100 106 10 124 58

STPT(10)	1299487782771071891	0 2 6 8 48 50 90 92 96 98	-1040659928370
STPT(10)	1299488288559950339	0 2 42 44 90 92 138 140 180 182	-534871049922
STPT(10)	1299488328955335689	0 2 18 20 30 32 42 44 60 62	-494475664572
SPT(16)	1299488418969616423	0 4 6 28 36 64 88 100 204 216 240 268 276 298 300 304	-404461383838
SPT(16)	1299488509973930257	0 4 34 60 76 112 142 160 186 204 234 270 286 312 342 346	-313457070004
STPT(10)	1299488719153044347	0 2 30 32 72 74 114 116 144 146	-104277955914
SPT(16)	1299488835176797637	0 30 42 50 66 92 114 116 210 212 234 260 276 284 296 326	11745797376
SPT(16)	1299489074782378033	0 46 64 154 196 210 214 250 270 306 310 324 366 456 474 520	251351377772
SPT(16)	1299489187969176983	0 114 116 186 204 224 246 258 296 308 330 350 368 438 440 554	364538176722
SPT(16)	1299489241034749693	0 36 40 60 66 78 106 120 154 168 196 208 214 234 238 274	417603749432
SPT(18)	1299489445777707007	0 6 24 36 42 52 64 90 136 150 196 222 234 244 250 262 280 286	622346706746