Prime p₀= 2946406872207912317 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 28 2 4 2 28 2 28 2 (?)
a_n: 0 2 42 44 84 86 114 116 120 122 150 152 180 182
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: ginga
db: batch=82, k=14, 40 40 28 4 28 28

SPT(16)	2946405059188363429	0 4 18 42 48 88 108 172 180 244 264 304 310 334 348 352	-1813019548888
SPT(16)	2946405457186618039	0 28 70 72 84 132 160 184 228 252 280 328 340 342 384 412	-1415021294278
SPT(16)	2946405489437629711	0 30 52 66 90 100 130 252 286 408 438 448 472 486 508 538	-1382770282606
SPT(16)	2946406080664989377	0 36 50 54 74 84 110 116 180 186 212 222 242 246 260 296	-791542922940
SPT(16)	2946406224915597293	0 14 36 78 80 84 104 120 134 150 170 174 176 218 240 254	-647292315024
STPT(10)	2946406867394071091	0 2 6 8 48 50 90 92 96 98	-4813841226
STPT(10)	2946407121511172321	0 2 30 32 60 62 90 92 120 122	249303260004
STPT(10)	2946407200476713159	0 2 42 44 90 92 138 140 180 182	328268800842
SPT(16)	2946407514010714477	0 10 22 64 66 196 204 246 280 322 330 460 462 504 516 526	641802802160
TPT(14)	2946407525555562119	0 2 60 62 78 80 102 104 120 122 252 254 270 272	653347649802
TPT(14)	2946408157199147747	0 2 12 14 30 32 54 56 72 74 150 152 162 164	1284991235430