Prime p₀= 794272768012717289 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 10 2 58 2 40 2 28 2 4 2 (?)
a_n: 0 2 18 20 30 32 90 92 132 134 162 164 168 170
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: 170
Found by: [SG]FX
db: batch=73, k=14, 16 10 58 40 28 4

SPT(16)	794272060679988791	0 26 62 98 108 120 162 182 216 236 278 290 300 336 372 398	-707332728498
TPT(14)	794272135141528031	0 2 18 20 30 32 126 128 156 158 216 218 228 230	-632871189258
TPT(14)	794272383734969309	0 2 30 32 60 62 132 134 210 212 240 242 252 254	-384277747980
SPT(16)	794272487365961651	0 6 60 102 126 150 152 176 192 216 218 242 266 308 362 368	-280646755638
SPT(16)	794272523106238321	0 52 82 90 112 126 132 136 162 166 172 186 208 216 246 298	-244906478968
TPT(14)	794272644998385569	0 2 78 80 132 134 162 164 168 170 282 284 288 290	-123014331720
STPT(10)	794272905096576419	0 2 48 50 90 92 132 134 180 182	137083859130
SPT(20)	794273126282832467	0 24 62 102 104 116 174 176 182 204 272 294 300 302 360 372 374 414 452 476	358270115178
STPT(10)	794273130310838537	0 2 60 62 72 74 84 86 144 146	362298121248
SPT(16)	794273419362579661	0 30 36 60 72 82 88 96 112 120 126 136 148 172 178 208	651349862372
SPT(16)	794273494409886487	0 6 124 132 156 250 276 292 294 310 336 430 454 462 580 586	726397169198