Prime p₀= 1424969842736752841 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 28 2 106 2 82 2 94 2 40 2 (?)
a_n: 0 2 18 20 48 50 156 158 240 242 336 338 378 380
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: 380
Found by: Theadalus
db: batch=78, k=14, 16 28 106 82 94 40

SPT(16)	1424969071744560469	0 24 40 52 72 102 144 150 184 190 232 262 282 294 310 334	-770992192372
SPT(16)	1424969076718299253	0 18 40 88 120 130 148 150 166 168 186 196 228 276 298 316	-766018453588
SPT(16)	1424969084537933947	0 46 52 90 96 132 210 220 246 256 334 370 376 414 420 466	-758198818894
STPT(10)	1424969190015633047	0 2 30 32 60 62 90 92 120 122	-652721119794
SPT(16)	1424969200435728109	0 24 28 40 54 60 78 114 178 214 232 238 252 264 268 292	-642301024732
STPT(10)	1424969360052970559	0 2 18 20 60 62 102 104 120 122	-482683782282
STPT(10)	1424970203210906279	0 2 12 14 90 92 168 170 180 182	360474153438
STPT(10)	1424970253939027919	0 2 12 14 30 32 48 50 60 62	411202275078
SPT(16)	1424970408631142993	0 8 50 86 114 120 140 170 174 204 224 230 258 294 336 344	565894390152
SPT(16)	1424970450180591031	0 48 72 100 112 120 132 138 142 148 160 168 180 208 232 280	607443838190
STPT(10)	1424970459681899057	0 2 54 56 72 74 90 92 144 146	616945146216