Prime p₀= 743876470744780229 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 4 2 58 2 28 2 22 2 16 2 (?)
a_n: 0 2 42 44 48 50 108 110 138 140 162 164 180 182
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: 182
Found by: Theadalus
db: batch=73, k=14, 40 4 58 28 22 16

TPT(14)	743875989553763321	0 2 6 8 78 80 90 92 126 128 138 140 180 182	-481191016908
STPT(10)	743876045474829497	0 2 24 26 42 44 60 62 84 86	-425269950732
STPT(10)	743876089476022157	0 2 12 14 72 74 132 134 144 146	-381268758072
SPT(16)	743876121642162959	0 20 30 50 62 102 140 150 182 192 230 270 282 302 312 332	-349102617270
SPT(16)	743876305861533967	0 72 96 136 166 202 210 234 292 316 324 360 390 430 454 526	-164883246262
SPT(16)	743876307829069201	0 22 52 70 100 138 166 246 322 402 430 468 498 516 546 568	-162915711028
STPT(10)	743876652896793539	0 2 12 14 30 32 48 50 60 62	182152013310
SPT(16)	743876712182545327	0 12 36 64 100 102 196 210 226 240 334 336 372 400 424 436	241437765098
SPT(16)	743876844678916423	0 4 18 24 54 88 126 138 166 178 216 250 280 286 300 304	373934136194
STPT(10)	743876882064593441	0 2 66 68 108 110 150 152 216 218	411319813212
SPT(16)	743876960907168653	0 60 78 90 116 134 138 224 270 356 360 378 404 416 434 494	490162388424