Prime p₀= 1267817550504889919 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 10 2 16 2 10 2 58 2 40 2 (?)
a_n: 0 2 108 110 120 122 138 140 150 152 210 212 252 254
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: 254
Found by: Megacruncher
db: batch=77, k=14, 106 10 16 10 58 40

SPT(16)	1267816609077927829	0 4 34 40 70 88 120 180 232 292 324 342 372 378 408 412	-941426962090
SPT(16)	1267816794307240693	0 18 24 40 66 76 130 204 220 294 348 358 384 400 406 424	-756197649226
SPT(16)	1267816968125401943	0 6 60 84 96 116 138 168 236 266 288 308 320 344 398 404	-582379487976
STPT(10)	1267817025262356377	0 2 30 32 42 44 54 56 84 86	-525242533542
SPT(16)	1267817047992423167	0 12 26 110 114 144 182 186 260 264 302 332 336 420 434 446	-502512466752
TPT(14)	1267817396318563061	0 2 168 170 186 188 228 230 270 272 306 308 318 320	-154186326858
STPT(12)	1267817860016177747	0 2 12 14 54 56 60 62 102 104 114 116	309511287828
STPT(12)	1267817973314005301	0 2 66 68 138 140 198 200 270 272 336 338	422809115382
TPT(14)	1267818104561073509	0 2 42 44 90 92 210 212 222 224 300 302 318 320	554056183590
SPT(16)	1267818308171008577	0 26 84 86 92 114 146 176 300 330 362 384 390 392 450 476	757666118658
SPT(16)	1267818814078572937	0 10 60 114 126 150 210 256 264 310 370 394 406 460 510 520	1263573683018