Prime p₀= 1286511689534070917 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 148 2 28 2 88 2 40 2 34 2 (?)
a_n: 0 2 12 14 162 164 192 194 282 284 324 326 360 362
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: 362
Found by: Theadalus
db: batch=77, k=14, 10 148 28 88 40 34

SPT(16)	1286510508982095311	0 6 26 56 90 92 116 120 158 162 186 188 222 252 272 278	-1180551975606
STPT(10)	1286510845286409539	0 2 18 20 30 32 42 44 60 62	-844247661378
TPT(14)	1286511104492205281	0 2 30 32 60 62 96 98 138 140 258 260 306 308	-585041865636
SPT(16)	1286511127119439427	0 56 86 90 92 114 140 176 420 456 482 504 506 510 540 596	-562414631490
SPT(16)	1286511563522494577	0 14 30 42 50 72 74 92 114 132 134 156 164 176 192 206	-126011576340
SPT(16)	1286511626932740581	0 18 48 50 120 128 140 158 270 288 300 308 378 380 410 428	-62601330336
SPT(16)	1286512310509513531	0 12 16 36 90 132 162 166 192 196 226 268 322 342 346 358	620975442614
STPT(10)	1286512571980184951	0 2 78 80 108 110 138 140 216 218	882446114034
STPT(10)	1286512667027232059	0 2 18 20 30 32 42 44 60 62	977493161142
STPT(10)	1286512780349844497	0 2 72 74 102 104 132 134 204 206	1090815773580
SPT(16)	1286513241653569913	0 48 98 104 144 146 156 170 174 188 198 200 240 246 296 344	1552119498996