Prime p₀= 1264415423084885681 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 10 2 28 2 46 2 10 2 196 2 (?)
a_n: 0 2 108 110 120 122 150 152 198 200 210 212 408 410
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: 410
Found by: Megacruncher
db: batch=77, k=14, 106 10 28 46 10 196

SPT(16)	1264414455925701331	0 28 72 82 88 96 102 132 136 166 172 180 186 196 240 268	-967159184350
SPT(16)	1264414640272112519	0 42 54 78 180 192 218 224 348 354 380 392 494 518 530 572	-782812773162
SPT(16)	1264414702391225683	0 60 64 154 168 216 226 238 246 258 268 316 330 420 424 484	-720693659998
SPT(16)	1264414797872264461	0 12 16 40 42 90 142 156 166 180 232 280 282 306 310 322	-625212621220
STPT(10)	1264414947194186267	0 2 30 32 42 44 54 56 84 86	-475890699414
SPT(16)	1264415058579375653	0 14 18 140 146 168 188 230 264 306 326 348 354 476 480 494	-364505510028
STPT(10)	1264415561621344577	0 2 30 32 42 44 54 56 84 86	138536458896
STPT(10)	1264416153180711239	0 2 42 44 60 62 78 80 120 122	730095825558
SPT(18)	1264416527203746517	0 6 34 76 82 94 96 112 124 252 264 280 282 294 300 342 370 376	1104118860836
SPT(16)	1264416971532835411	0 22 42 90 100 120 148 162 166 180 208 228 238 286 306 328	1548447949730
STPT(10)	1264417002464487869	0 2 48 50 90 92 132 134 180 182	1579379602188