Prime p₀= 1267721384096422601 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 28 2 10 2 10 2 34 2 22 2 (?)
a_n: 0 2 36 38 66 68 78 80 90 92 126 128 150 152
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: 152
Found by: Megacruncher
db: batch=77, k=14, 34 28 10 10 34 22

SPT(16)	1267720295536467169	0 40 102 160 180 204 238 244 258 264 298 322 342 400 462 502	-1088559955432
STPT(10)	1267720624410239141	0 2 6 8 18 20 30 32 36 38	-759686183460
SPT(16)	1267720910144614543	0 28 70 76 100 114 118 150 154 186 190 204 228 234 276 304	-473951808058
SPT(16)	1267721099261369881	0 6 10 46 58 90 100 156 172 228 238 270 282 318 322 328	-284835052720
SPT(16)	1267721139138608173	0 28 54 76 88 94 96 160 264 328 330 336 348 370 396 424	-244957814428
SPT(16)	1267721361653507557	0 10 40 60 66 112 144 156 250 262 294 340 346 366 396 406	-22442915044
SPT(16)	1267721646548215457	0 44 74 102 120 126 132 134 252 254 260 266 284 312 342 386	262451792856
SPT(16)	1267721976602188223	0 36 68 86 90 128 158 168 188 198 228 266 270 288 320 356	592505765622
SPT(16)	1267722138506347177	0 10 12 30 54 124 142 154 162 174 192 262 286 304 306 316	754409924576
STPT(10)	1267722209856529949	0 2 18 20 30 32 42 44 60 62	825760107348
SPT(16)	1267722268239626197	0 22 70 84 120 174 202 220 234 252 280 334 370 384 432 454	884143203596