Prime p₀= 780927269079849581 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 184 2 28 2 22 2 136 2 10 2 28 2 (?)
a_n: 0 2 186 188 216 218 240 242 378 380 390 392 420 422
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: 422
Found by: [SG]steini
db: batch=73, k=14, 184 28 22 136 10 28

SPT(16)	780926889246052259	0 2 60 78 132 162 170 198 242 270 278 308 362 380 438 440	-379833797322
SPT(16)	780926964281359627	0 6 34 40 46 70 102 186 190 274 306 330 336 342 370 376	-304798489954
SPT(16)	780927051983601781	0 12 52 82 96 102 112 126 142 156 166 172 186 216 256 268	-217096247800
STPT(10)	780927080124549857	0 2 42 44 72 74 102 104 144 146	-188955299724
STPT(10)	780927087068432327	0 2 72 74 102 104 132 134 204 206	-182011417254
SPT(16)	780927265511918617	0 4 24 46 70 72 100 102 154 156 184 186 210 232 252 256	-3567930964
SPT(16)	780927499219311757	0 34 40 60 70 82 84 126 130 172 174 186 196 216 222 256	230139462176
SPT(16)	780927517046103853	0 18 34 48 76 88 114 130 264 280 306 318 346 360 376 394	247966254272
SPT(16)	780927705442042649	0 12 38 74 108 122 140 152 210 222 240 254 288 324 350 362	436362193068
STPT(10)	780927713407860719	0 2 42 44 120 122 198 200 240 242	444328011138
TPT(14)	780927713776685549	0 2 18 20 42 44 198 200 228 230 252 254 258 260	444696835968