Prime p₀= 817123696306773857 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 94 2 28 2 22 2 4 2 (?)
a_n: 0 2 42 44 84 86 180 182 210 212 234 236 240 242
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: 242
Found by: [SG]FX
db: batch=73, k=14, 40 40 94 28 22 4

STPT(10)	817123212143559941	0 2 6 8 48 50 90 92 96 98	-484163213916
SPT(16)	817123528374211753	0 10 24 28 88 90 168 184 204 220 298 300 360 364 378 388	-167932562104
TPT(14)	817123572293734547	0 2 30 32 90 92 114 116 174 176 240 242 294 296	-124013039310
SPT(16)	817123627508007983	0 14 38 48 66 78 158 164 210 216 296 308 326 336 360 374	-68798765874
TPT(14)	817123641213709187	0 2 24 26 42 44 54 56 150 152 204 206 210 212	-55093064670
SPT(16)	817123679822984173	0 6 58 120 160 264 274 280 294 300 310 414 454 516 568 574	-16483789684
STPT(10)	817124194089151811	0 2 36 38 78 80 120 122 156 158	497782377954
SPT(16)	817124309844285013	0 30 106 114 204 256 270 280 324 334 348 400 490 498 574 604	613537511156
SPT(16)	817124587029330413	0 18 54 78 120 164 168 194 234 260 264 308 350 374 410 428	890722556556
STPT(10)	817124625281685947	0 2 30 32 72 74 114 116 144 146	928974912090
STPT(10)	817124742076812887	0 2 84 86 132 134 180 182 264 266	1045770039030