Prime p₀= 1267768406805549029 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 28 2 22 2 118 2 76 2 10 2 (?)
a_n: 0 2 78 80 108 110 132 134 252 254 330 332 342 344
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: 344
Found by: Megacruncher
db: batch=77, k=14, 76 28 22 118 76 10

STPT(10)	1267767063183699191	0 2 36 38 78 80 120 122 156 158	-1343621849838
STPT(12)	1267767253570192379	0 2 12 14 42 44 138 140 168 170 180 182	-1153235356650
STPT(10)	1267767348501772187	0 2 24 26 42 44 60 62 84 86	-1058303776842
SPT(16)	1267767773040649171	0 12 18 78 118 130 168 180 238 250 288 300 340 400 406 418	-633764899858
TPT(14)	1267768260984695147	0 2 30 32 84 86 240 242 294 296 390 392 402 404	-145820853882
STPT(10)	1267768302404655671	0 2 6 8 48 50 90 92 96 98	-104400893358
STPT(10)	1267768894006484897	0 2 30 32 42 44 54 56 84 86	487200935868
SPT(16)	1267769277252036589	0 4 24 30 42 70 114 130 132 148 192 220 232 238 258 262	870446487560
SPT(16)	1267769413139072293	0 10 28 46 66 90 130 150 196 216 256 280 300 318 336 346	1006333523264
TPT(14)	1267769722170639641	0 2 18 20 30 32 48 50 126 128 186 188 198 200	1315365090612
SPT(16)	1267769940558254279	0 32 38 42 72 98 108 168 182 242 252 278 308 312 318 350	1533752705250