Prime p₀= 2378187368731994471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 112 2 154 2 100 2 10 2 76 2 (?)
a_n: 0 2 36 38 150 152 306 308 408 410 420 422 498 500
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: 500
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 34 112 154 100 10 76

SPT(16)	2378185448341162133	0 18 20 48 66 120 150 156 218 224 254 308 326 354 356 374	-1920390832338
STPT(12)	2378185627943675687	0 2 12 14 42 44 102 104 132 134 144 146	-1740788318784
STPT(10)	2378185655451657767	0 2 42 44 72 74 102 104 144 146	-1713280336704
STPT(10)	2378185950115621727	0 2 42 44 72 74 102 104 144 146	-1418616372744
STPT(10)	2378185952816192927	0 2 72 74 102 104 132 134 204 206	-1415915801544
STPT(10)	2378186505203056019	0 2 42 44 90 92 138 140 180 182	-863528938452
STPT(10)	2378187635678373731	0 2 36 38 78 80 120 122 156 158	266946379260
STPT(12)	2378188034359254527	0 2 12 14 42 44 102 104 132 134 144 146	665627260056
SPT(16)	2378188075410596599	0 52 90 118 132 148 168 174 238 244 264 280 294 322 360 412	706678602128
SPT(16)	2378188138701184357	0 10 42 64 70 84 94 126 130 162 172 186 192 214 246 256	769969189886
SPT(16)	2378188285040400851	0 50 56 90 98 146 168 186 200 218 240 288 296 330 336 386	916308406380