Prime p₀= 859586914823181119 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 28 2 16 2 52 2 16 2 10 2 (?)
a_n: 0 2 120 122 150 152 168 170 222 224 240 242 252 254
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: 254
Found by: suriv
db: batch=73, k=14, 118 28 16 52 16 10

SPT(16)	859586340918022217	0 14 42 66 80 90 104 110 126 132 146 156 170 194 222 236	-573905158902
SPT(16)	859586412749151709	0 40 42 48 84 88 102 150 202 250 264 268 304 310 312 352	-502074029410
STPT(10)	859586457644514401	0 2 6 8 48 50 90 92 96 98	-457178666718
SPT(16)	859586534896365517	0 30 36 40 66 82 126 156 190 220 264 280 306 310 316 346	-379926815602
SPT(16)	859586577245832407	0 6 24 44 66 102 164 174 182 192 254 290 312 332 350 356	-337577348712
STPT(10)	859586615299992737	0 2 42 44 132 134 222 224 264 266	-299523188382
SPT(16)	859586926941402857	0 2 36 66 84 92 114 126 200 212 234 242 260 290 324 326	12118221738
SPT(16)	859587093700644847	0 16 52 66 72 90 150 154 222 226 286 304 310 324 360 376	178877463728
SPT(16)	859587111718493597	0 32 36 60 80 104 110 162 164 216 222 246 266 290 294 326	196895312478
STPT(10)	859587463393540547	0 2 12 14 42 44 72 74 84 86	548570359428
TPT(14)	859587621784238771	0 2 6 8 30 32 48 50 186 188 378 380 420 422	706961057652