Prime p₀= 2743641832005576659 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 100 2 28 2 28 2 76 2 28 2 (?)
a_n: 0 2 48 50 150 152 180 182 210 212 288 290 318 320
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: 320
Found by: Roadranner
db: batch=82, k=14, 46 100 28 28 76 28

SPT(16)	2743640353848968867	0 2 12 20 44 62 80 90 206 216 234 252 276 284 294 296	-1478156607792
STPT(10)	2743640401770194651	0 2 6 8 48 50 90 92 96 98	-1430235382008
SPT(16)	2743640488170309551	0 66 96 176 180 206 272 300 308 336 402 428 432 512 542 608	-1343835267108
STPT(10)	2743640592422781419	0 2 18 20 30 32 42 44 60 62	-1239582795240
SPT(16)	2743641215280074141	0 42 86 90 186 260 308 372 446 510 558 632 728 732 776 818	-616725502518
SPT(16)	2743641330208342247	0 32 60 80 116 140 146 162 164 180 186 210 246 266 294 326	-501797234412
SPT(16)	2743641876418464293	0 18 24 30 44 60 90 98 156 164 194 210 224 230 236 254	44412887634
SPT(16)	2743642370632711183	0 54 58 126 138 154 168 174 220 226 240 256 268 336 340 394	538627134524
STPT(10)	2743642377843959489	0 2 18 20 60 62 102 104 120 122	545838382830
STPT(10)	2743642519205653139	0 2 42 44 90 92 138 140 180 182	687200076480
STPT(12)	2743642803124476359	0 2 30 32 72 74 78 80 120 122 150 152	971118899700