Prime p₀= 1264417123871244947 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 16 2 106 2 28 2 22 2 28 2 (?)
a_n: 0 2 114 116 132 134 240 242 270 272 294 296 324 326
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: 326
Found by: Megacruncher
db: batch=77, k=14, 112 16 106 28 22 28

TPT(14)	1264415423084885681	0 2 108 110 120 122 150 152 198 200 210 212 408 410	-1700786359266
STPT(10)	1264415561621344577	0 2 30 32 42 44 54 56 84 86	-1562249900370
STPT(10)	1264416153180711239	0 2 42 44 60 62 78 80 120 122	-970690533708
SPT(18)	1264416527203746517	0 6 34 76 82 94 96 112 124 252 264 280 282 294 300 342 370 376	-596667498430
SPT(16)	1264416971532835411	0 22 42 90 100 120 148 162 166 180 208 228 238 286 306 328	-152338409536
STPT(10)	1264417002464487869	0 2 48 50 90 92 132 134 180 182	-121406757078
SPT(16)	1264417374906517607	0 32 72 86 116 144 146 152 174 180 182 210 240 254 294 326	251035272660
SPT(16)	1264418068347226829	0 12 14 32 38 44 72 84 98 110 138 144 150 168 170 182	944475981882
STPT(10)	1264418235698701337	0 2 72 74 102 104 132 134 204 206	1111827456390
SPT(16)	1264418501385596827	0 30 34 40 46 54 70 90 166 186 202 210 216 222 226 256	1377514351880
SPT(16)	1264418875673018827	0 16 24 66 76 84 100 136 150 186 202 210 220 262 270 286	1751801773880