Prime p₀= 1086267538544566319 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 208 2 28 2 28 2 40 2 4 2 (?)
a_n: 0 2 30 32 240 242 270 272 300 302 342 344 348 350
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: 350
Found by: [SG]ATA-Rolf
db: batch=76, k=14, 28 208 28 28 40 4

STPT(10)	1086265964847555641	0 2 30 32 120 122 210 212 240 242	-1573697010678
STPT(12)	1086266021672011457	0 2 12 14 54 56 90 92 132 134 144 146	-1516872554862
TPT(14)	1086266279150621747	0 2 12 14 90 92 162 164 180 182 204 206 222 224	-1259393944572
STPT(10)	1086266382053597411	0 2 6 8 18 20 30 32 36 38	-1156490968908
SPT(16)	1086267189743032991	0 36 68 122 150 156 168 210 248 290 302 308 336 390 422 458	-348801533328
SPT(16)	1086267470001766411	0 52 90 102 126 132 172 178 210 216 256 262 286 298 336 388	-68542799908
SPT(16)	1086267838545685837	0 4 10 42 112 114 130 142 144 156 172 174 244 276 282 286	300001119518
STPT(10)	1086267980014868237	0 2 30 32 72 74 114 116 144 146	441470301918
SPT(16)	1086267981112947943	0 6 10 48 60 70 76 100 204 228 234 244 256 294 298 304	442568381624
SPT(16)	1086267999088025291	0 2 20 26 30 32 108 168 170 230 306 308 312 318 336 338	460543458972
STPT(10)	1086268202910254237	0 2 30 32 42 44 54 56 84 86	664365687918