Prime p₀= 2113139434655368829 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 58 2 22 2 124 2 70 2 16 2 (?)
a_n: 0 2 78 80 138 140 162 164 288 290 360 362 378 380
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: 380
Found by: [SG-2W]Kurzer
db: batch=80, k=14, 76 58 22 124 70 16

SPT(16)	2113138683355961293	0 4 40 60 118 120 184 204 250 270 334 336 394 414 450 454	-751299407536
STPT(10)	2113139018218406999	0 2 18 20 30 32 42 44 60 62	-416436961830
SPT(16)	2113139106777042263	0 8 44 56 110 128 134 170 174 210 216 234 288 300 336 344	-327878326566
SPT(16)	2113139111568997639	0 24 54 88 112 142 144 154 168 178 180 210 234 268 298 322	-323086371190
SPT(16)	2113139126408485907	0 12 54 56 72 102 120 140 156 176 194 224 240 242 284 296	-308246882922
STPT(10)	2113139184546911837	0 2 84 86 162 164 240 242 324 326	-250108456992
TPT(14)	2113139700886016807	0 2 30 32 54 56 132 134 210 212 270 272 294 296	266230647978
SPT(16)	2113139795473846723	0 30 48 126 160 174 180 216 268 304 310 324 358 436 454 484	360818477894
SPT(16)	2113139833290538529	0 14 44 50 74 152 164 170 234 240 252 330 354 360 390 404	398635169700
STPT(10)	2113140544395047267	0 2 90 92 102 104 114 116 204 206	1109739678438
SPT(16)	2113140706064889337	0 4 40 42 72 90 106 130 156 180 196 214 244 246 282 286	1271409520508