Prime p₀= 779090261891000957 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 16 2 10 2 70 2 16 2 (?)
a_n: 0 2 30 32 42 44 60 62 72 74 144 146 162 164
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: 164
Found by: Ralfy
db: batch=73, k=14, 28 10 16 10 70 16

SPT(13)	779089297826429617	0 24 126 144 180 186 210 234 240 276 294 396 420	-964064571340
SPT(16)	779089308767662559	0 14 62 78 80 84 122 134 198 210 248 252 254 270 318 332	-953123338398
SPT(16)	779089519880125217	0 2 24 54 60 80 110 114 152 156 186 206 212 242 264 266	-742010875740
SPT(16)	779089573715647619	0 20 50 60 78 90 98 104 138 144 152 164 182 192 222 242	-688175353338
SPT(16)	779090044140089477	0 14 32 56 60 90 92 122 144 174 176 206 210 234 252 266	-217750911480
SPT(16)	779090135174414471	0 6 38 90 102 108 126 140 168 182 200 206 218 270 302 308	-126716586486
SPT(16)	779090262619327843	0 18 66 130 156 220 226 246 268 288 294 358 384 448 496 514	728326886
STPT(10)	779090364089198279	0 2 18 20 30 32 42 44 60 62	102198197322
TPT(14)	779090815093232027	0 2 42 44 72 74 84 86 192 194 222 224 234 236	553202231070
SPT(16)	779091108591766627	0 34 40 52 82 90 172 184 210 222 304 312 342 354 360 394	846700765670
SPT(16)	779091136639979771	0 2 18 26 56 60 86 138 170 222 248 252 282 290 306 308	874748978814