Prime p₀= 2341487101693612667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 46 2 40 2 136 2 10 2 58 2 (?)
a_n: 0 2 84 86 132 134 174 176 312 314 324 326 384 386
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: 386
Found by: Landjunge
db: batch=81, k=14, 82 46 40 136 10 58

SPT(16)	2341486618643439937	0 54 60 64 66 70 102 106 150 154 186 190 192 196 202 256	-483050172730
SPT(16)	2341486725778705697	0 2 36 44 54 56 86 90 296 300 330 332 342 350 384 386	-375914906970
STPT(10)	2341486777044350207	0 2 30 32 42 44 54 56 84 86	-324649262460
SPT(16)	2341486933790616281	0 8 48 90 92 152 180 192 206 218 246 306 308 350 390 398	-167902996386
SPT(16)	2341486962759989813	0 18 30 48 54 86 126 230 234 338 378 410 416 434 446 464	-138933622854
SPT(16)	2341486963164642967	0 4 42 60 64 76 112 130 216 234 270 282 286 304 342 346	-138528969700
SPT(16)	2341487145046434883	0 16 24 66 78 106 124 136 168 180 198 226 238 280 288 304	43352822216
STPT(10)	2341487258150283557	0 2 12 14 42 44 72 74 84 86	156456670890
SPT(16)	2341487288522015173	0 4 16 30 46 60 66 114 310 358 364 378 394 408 420 424	186828402506
SPT(16)	2341487468416258901	0 32 62 68 72 90 242 270 380 408 560 578 582 588 618 650	366722646234
SPT(13)	2341487470651328551	0 12 18 48 60 168 180 192 300 312 342 348 360	368957715884