Prime p₀= 3006124507611593909 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 40 2 76 2 100 2 178 2 (?)
a_n: 0 2 30 32 90 92 132 134 210 212 312 314 492 494
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: 494
Found by: conf [MM]
db: batch=82, k=14, 28 58 40 76 100 178

SPT(16)	3006124006821274081	0 10 18 46 52 66 72 96 112 136 142 156 162 190 198 208	-500790319828
SPT(16)	3006124048936362229	0 22 28 42 82 178 198 208 222 232 252 348 388 402 408 430	-458675231680
SPT(16)	3006124139315951669	0 8 72 78 140 162 164 212 240 288 290 312 374 380 444 452	-368295642240
STPT(10)	3006124229913012587	0 2 30 32 42 44 54 56 84 86	-277698581322
SPT(16)	3006124255322119163	0 14 26 30 60 84 86 116 138 168 170 194 224 228 240 254	-252289474746
SPT(16)	3006124449510183283	0 28 58 64 78 84 100 148 150 198 214 220 234 240 270 298	-58101410626
STPT(10)	3006124798741428179	0 2 12 14 30 32 48 50 60 62	291129834270
SPT(16)	3006124922807912579	0 24 44 78 92 122 164 174 248 258 300 330 344 378 398 422	415196318670
SPT(16)	3006124929591943931	0 36 56 66 78 80 102 122 126 146 168 170 182 192 212 248	421980350022
SPT(16)	3006125162888197957	0 34 76 154 166 172 220 222 244 246 294 300 312 390 432 466	655276604048
STPT(10)	3006125587258159979	0 2 18 20 30 32 42 44 60 62	1079646566070