Prime p₀= 1568956671366516449 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 40 2 4 2 112 2 88 2 4 2 (?)
a_n: 0 2 90 92 132 134 138 140 252 254 342 344 348 350
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: crashtech
db: batch=78, k=14, 88 40 4 112 88 4

STPT(10)	1568955731334839537	0 2 30 32 42 44 54 56 84 86	-940031676912
STPT(10)	1568955981711235487	0 2 30 32 42 44 54 56 84 86	-689655280962
TPT(14)	1568956043993051801	0 2 6 8 36 38 90 92 96 98 126 128 150 152	-627373464648
STPT(10)	1568956105579466159	0 2 48 50 90 92 132 134 180 182	-565787050290
SPT(16)	1568956448768108417	0 14 20 56 62 110 122 162 194 234 246 294 300 336 342 356	-222598408032
SPT(16)	1568956527039868387	0 4 12 16 40 46 84 106 120 142 180 186 210 214 222 226	-144326648062
SPT(16)	1568956814812137581	0 6 48 122 152 182 186 228 230 272 276 306 336 410 452 458	143445621132
SPT(16)	1568956833497944441	0 18 36 48 70 78 106 148 150 192 220 228 250 262 280 298	162131427992
SPT(16)	1568957391494488273	0 24 46 64 108 126 144 160 204 220 238 256 300 318 340 364	720127971824
STPT(10)	1568957848502749091	0 2 30 32 78 80 126 128 156 158	1177136232642
SPT(16)	1568958033587806153	0 4 10 36 40 64 66 106 168 208 210 234 238 264 270 274	1362221289704