Prime p₀= 3008725324585482179 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 64 2 58 2 22 2 4 2 40 2 (?)
a_n: 0 2 42 44 108 110 168 170 192 194 198 200 240 242
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: 242
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 40 64 58 22 4 40

SPT(16)	3008723151037471757	0 14 24 32 36 42 84 102 134 152 194 200 204 212 222 236	-2173548010422
TPT(14)	3008723568268661807	0 2 90 92 102 104 114 116 210 212 384 386 462 464	-1756316820372
SPT(16)	3008723743183170107	0 20 32 60 96 104 186 240 326 380 462 470 506 534 546 566	-1581402312072
SPT(16)	3008723767918484639	0 18 50 74 80 122 144 210 242 308 330 372 378 402 434 452	-1556666997540
SPT(16)	3008724532722904451	0 36 78 80 126 140 170 176 360 366 396 410 456 458 500 536	-791862577728
STPT(10)	3008725198979040719	0 2 12 14 90 92 168 170 180 182	-125606441460
STPT(12)	3008725669174958417	0 2 12 14 42 44 150 152 180 182 192 194	344589476238
SPT(16)	3008725681350002353	0 36 70 120 136 174 178 270 304 396 400 438 454 504 538 574	356764520174
SPT(16)	3008725738544549003	0 8 50 66 80 158 170 194 210 234 246 324 338 354 396 404	413959066824
SPT(16)	3008725990984872667	0 4 22 60 64 84 112 126 130 144 172 192 196 234 252 256	666399390488
SPT(16)	3008726282544061181	0 18 152 200 222 258 278 302 306 330 350 386 408 456 590 608	957958579002