Prime p₀= 817127041588278299 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 94 2 130 2 118 2 70 2 28 2 (?)
a_n: 0 2 72 74 168 170 300 302 420 422 492 494 522 524
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: 524
Found by: [SG]FX
db: batch=73, k=14, 70 94 130 118 70 28

SPT(16)	817126294998981559	0 12 28 34 54 60 72 82 120 130 142 148 168 174 190 202	-746589296740
SPT(16)	817126341781586831	0 2 8 26 66 126 156 212 246 302 332 392 432 450 456 458	-699806691468
STPT(10)	817126369783327361	0 2 6 8 18 20 30 32 36 38	-671804950938
SPT(16)	817126379276290483	0 10 30 54 58 70 88 154 294 360 378 390 394 418 438 448	-662311987816
TPT(14)	817126392932374739	0 2 30 32 90 92 102 104 132 134 258 260 348 350	-648655903560
STPT(10)	817126535802134417	0 2 30 32 72 74 114 116 144 146	-505786143882
SPT(16)	817127136505394137	0 10 34 36 40 66 96 100 216 220 250 276 280 282 306 316	94917115838
TPT(14)	817127253103100741	0 2 18 20 156 158 168 170 180 182 306 308 510 512	211514822442
SPT(16)	817127267235193949	0 14 20 30 42 180 194 212 240 258 272 410 422 432 438 452	225646915650
SPT(16)	817127440449252607	0 10 30 42 54 70 72 76 90 94 96 112 124 136 156 166	398860974308
SPT(16)	817127491044187039	0 10 22 72 78 148 150 210 220 280 282 352 358 408 420 430	449455908740