Prime p₀= 1314067726349673017 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 40 2 16 2 148 2 88 2 40 2 (?)
a_n: 0 2 72 74 114 116 132 134 282 284 372 374 414 416
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: 416
Found by: Theadalus
db: batch=77, k=14, 70 40 16 148 88 40

STPT(10)	1314066279010193381	0 2 30 32 78 80 126 128 156 158	-1447339479636
SPT(16)	1314066403266798989	0 62 78 84 108 110 122 132 140 150 162 164 188 194 210 272	-1323082874028
SPT(16)	1314066533109244393	0 36 66 84 118 120 150 178 216 244 274 276 310 328 358 394	-1193240428624
STPT(10)	1314066891363735371	0 2 30 32 78 80 126 128 156 158	-834985937646
SPT(16)	1314067032348822527	0 44 114 116 122 132 150 156 200 206 224 234 240 242 312 356	-694000850490
SPT(16)	1314067204772895829	0 40 42 48 54 72 88 172 240 324 340 358 364 370 372 412	-521576777188
SPT(16)	1314067921388095787	0 12 36 44 110 116 146 174 182 210 240 246 312 320 344 356	195038422770
TPT(14)	1314067927908075497	0 2 42 44 174 176 180 182 330 332 510 512 570 572	201558402480
SPT(16)	1314068084234277221	0 92 126 128 146 182 188 198 230 240 246 282 300 302 336 428	357884604204
SPT(16)	1314068493635539679	0 14 24 30 38 48 108 134 198 224 284 294 302 308 318 332	767285866662
STPT(10)	1314068497318026209	0 2 12 14 90 92 168 170 180 182	770968353192