Prime p₀= 3008828078861458937 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 4 2 178 2 10 2 88 2 (?)
a_n: 0 2 12 14 24 26 30 32 210 212 222 224 312 314
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: 314
Found by: Orange Kid
db: batch=82, k=14, 10 10 4 178 10 88

SPT(16)	3008826802292184281	0 48 50 72 90 132 146 168 170 192 206 248 266 288 290 338	-1276569274656
SPT(16)	3008826984483500501	0 66 90 102 128 140 168 192 206 230 258 270 296 308 332 398	-1094377958436
STPT(10)	3008827018703795579	0 2 12 14 90 92 168 170 180 182	-1060157663358
SPT(16)	3008827557576128747	0 6 12 86 90 110 140 144 182 186 216 236 240 314 320 326	-521285330190
SPT(16)	3008827681490350393	0 10 16 18 24 46 88 94 120 126 168 190 196 198 204 214	-397371108544
STPT(10)	3008827973756512001	0 2 6 8 48 50 90 92 96 98	-105104946936
STPT(10)	3008828240386484981	0 2 48 50 108 110 168 170 216 218	161525026044
STPT(10)	3008828349233035169	0 2 42 44 120 122 198 200 240 242	270371576232
SPT(16)	3008828598443987401	0 10 12 82 96 102 130 148 150 168 196 202 216 286 288 298	519582528464
SPT(16)	3008828887583816611	0 18 30 42 72 88 100 108 130 138 150 166 196 208 220 238	808722357674
SPT(18)	3008829162016334537	0 24 44 66 114 174 222 236 242 264 270 284 332 392 440 462 482 506	1083154875600