Prime p₀= 1245296387657008031 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 28 2 40 2 166 2 136 2 40 2 (?)
a_n: 0 2 48 50 78 80 120 122 288 290 426 428 468 470
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: 470
Found by: Megacruncher
db: batch=77, k=14, 46 28 40 166 136 40

STPT(10)	1245294601793341367	0 2 90 92 102 104 114 116 204 206	-1785863666664
SPT(16)	1245294919221868483	0 16 34 70 94 126 184 196 198 210 268 300 324 360 378 394	-1468435139548
TPT(14)	1245295224904610861	0 2 48 50 60 62 78 80 90 92 120 122 126 128	-1162752397170
STPT(10)	1245295618246094939	0 2 18 20 30 32 42 44 60 62	-769410913092
TPT(14)	1245295765878021629	0 2 72 74 102 104 168 170 228 230 270 272 300 302	-621778986402
SPT(16)	1245296336225220043	0 10 64 78 84 108 136 144 160 168 196 220 226 240 294 304	-51431787988
SPT(16)	1245296711839954621	0 52 60 78 100 106 172 210 298 336 402 408 430 448 456 508	324182946590
SPT(16)	1245296913463298711	0 12 30 42 72 108 140 152 156 168 200 236 266 278 296 308	525806290680
SPT(16)	1245297228577554223	0 30 78 88 96 120 144 166 168 190 214 238 246 256 304 334	840920546192
STPT(10)	1245297563656927367	0 2 30 32 72 74 114 116 144 146	1175999919336
SPT(16)	1245297709018894649	0 2 30 72 74 132 138 200 252 314 320 378 380 422 450 452	1321361886618