Prime p₀= 2345654912254109387 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 28 2 40 2 46 2 76 2 172 2 (?)
a_n: 0 2 42 44 72 74 114 116 162 164 240 242 414 416
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: Xenon
db: batch=81, k=14, 40 28 40 46 76 172

SPT(16)	2345653598396156371	0 16 60 66 72 78 82 100 108 126 130 136 142 148 192 208	-1313857953016
SPT(16)	2345653606710820447	0 30 132 160 174 184 196 216 220 240 252 262 276 304 406 436	-1305543288940
SPT(16)	2345653646450975873	0 8 20 38 56 90 96 104 180 188 194 228 246 264 276 284	-1265803133514
SPT(16)	2345654009572698413	0 26 44 56 80 114 164 180 194 210 260 294 318 330 348 374	-902681410974
TPT(14)	2345654027361941717	0 2 12 14 42 44 114 116 120 122 150 152 180 182	-884892167670
STPT(10)	2345654855207429177	0 2 24 26 42 44 60 62 84 86	-57046680210
SPT(16)	2345655005867054633	0 14 48 50 96 104 126 138 206 218 240 248 294 296 330 344	93612945246
STPT(10)	2345655079446343307	0 2 30 32 42 44 54 56 84 86	167192233920
SPT(16)	2345655223320318599	0 2 20 50 72 134 140 152 240 252 258 320 342 372 390 392	311066209212
SPT(16)	2345656112531925929	0 38 42 60 102 108 168 198 212 242 302 308 350 368 372 410	1200277816542
SPT(16)	2345656758236532227	0 6 14 44 86 90 126 170 216 260 296 300 342 372 380 386	1845982422840