Prime p₀= 2014245726828142859 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 34 2 148 2 22 2 16 2 10 2 (?)
a_n: 0 2 42 44 78 80 228 230 252 254 270 272 282 284
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: 284
Found by: Landjunge
db: batch=80, k=14, 40 34 148 22 16 10

SPT(18)	2014245130175473049	0 98 114 140 158 264 290 294 368 444 518 522 548 654 672 698 714 812	-596652669810
SPT(16)	2014245269950934807	0 2 26 30 42 80 140 180 182 222 282 320 332 336 360 362	-456877208052
SPT(16)	2014245380344956481	0 6 22 52 88 90 130 178 270 318 358 360 396 426 442 448	-346483186378
SPT(16)	2014245448266900133	0 4 88 168 190 204 246 270 304 328 370 384 406 486 570 574	-278561242726
SPT(16)	2014245495131775559	0 10 52 64 70 78 132 168 274 310 364 372 378 390 432 442	-231696367300
SPT(16)	2014245600353421133	0 4 10 30 46 48 70 76 108 114 136 138 154 174 180 184	-126474721726
TPT(14)	2014246454391414779	0 2 30 32 72 74 132 134 180 182 240 242 258 260	727563271920
SPT(16)	2014246563103024829	0 12 14 54 80 90 120 134 150 164 194 204 230 270 272 284	836274881970
TPT(14)	2014246919009250491	0 2 18 20 66 68 96 98 150 152 168 170 228 230	1192181107632
SPT(16)	2014247007792156649	0 12 18 58 88 102 142 150 172 180 220 234 264 304 310 322	1280964013790
SPT(16)	2014247330863753729	0 64 90 94 168 178 184 190 198 204 210 220 294 298 324 388	1604035610870