Prime p₀= 4092750856663662371 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 28 2 70 2 28 2 10 2 64 2 (?)
a_n: 0 2 36 38 66 68 138 140 168 170 180 182 246 248
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: 248
Found by: [AF>WildWildWest]Sebastien
db: batch=84, k=14, 34 28 70 28 10 64

TPT(14)	4092749865807811301	0 2 18 20 36 38 60 62 78 80 90 92 120 122	-990855851070
SPT(16)	4092750197081681437	0 16 60 66 100 112 120 180 196 256 264 276 310 316 360 376	-659581980934
STPT(10)	4092750251155918019	0 2 48 50 90 92 132 134 180 182	-605507744352
SPT(16)	4092750491358333653	0 24 36 78 90 116 144 210 224 290 318 344 356 398 410 434	-365305328718
SPT(13)	4092750542742079601	0 36 126 138 168 258 318 378 468 498 510 600 636	-313921582770
STPT(10)	4092750545774243159	0 2 78 80 120 122 162 164 240 242	-310889419212
SPT(16)	4092750896798795663	0 38 60 68 80 90 104 126 158 180 194 204 216 224 246 284	40135133292
SPT(16)	4092750941933669789	0 2 44 54 68 98 200 222 230 252 354 384 398 408 450 452	85270007418
STPT(10)	4092751221741380249	0 2 18 20 60 62 102 104 120 122	365077717878
TPT(14)	4092751798163893517	0 2 30 32 42 44 132 134 174 176 210 212 240 242	941500231146
SPT(16)	4092751969898375689	0 10 12 22 24 90 100 112 120 132 142 208 210 220 222 232	1113234713318