Prime p₀= 1321097143249726637 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 70 2 46 2 40 2 46 2 40 2 (?)
a_n: 0 2 12 14 84 86 132 134 174 176 222 224 264 266
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: 266
Found by: Megacruncher
db: batch=77, k=14, 10 70 46 40 46 40

STPT(10)	1321095416119287629	0 2 18 20 30 32 42 44 60 62	-1727130439008
SPT(16)	1321095584209022669	0 54 98 120 132 144 164 194 258 288 308 320 332 354 398 452	-1559040703968
SPT(16)	1321096030503009359	0 20 44 60 74 78 132 144 158 170 224 228 242 258 282 302	-1112746717278
SPT(16)	1321096088177210489	0 44 60 102 134 140 162 170 174 182 204 210 242 284 300 344	-1055072516148
STPT(10)	1321096567755609647	0 2 30 32 60 62 90 92 120 122	-575494116990
SPT(16)	1321096875356358719	0 42 48 80 98 108 132 180 182 230 254 264 282 314 320 362	-267893367918
SPT(16)	1321097152148314253	0 26 98 110 138 164 180 278 336 434 450 476 504 516 588 614	8898587616
SPT(16)	1321097469172708523	0 14 18 44 50 84 98 116 168 186 200 234 240 266 270 284	325922981886
SPT(16)	1321097689031580041	0 18 32 96 126 140 158 222 266 330 348 362 392 456 470 488	545781853404
SPT(16)	1321097961093375229	0 4 30 102 154 162 174 204 268 298 310 318 370 442 468 472	817843648592
STPT(10)	1321098195182640527	0 2 42 44 72 74 102 104 144 146	1051932913890