Prime p₀= 2867953152058490729 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 16 2 22 2 58 2 46 2 76 2 (?)
a_n: 0 2 60 62 78 80 102 104 162 164 210 212 288 290
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: 290
Found by: JayPi
db: batch=82, k=14, 58 16 22 58 46 76

SPT(16)	2867952141610087517	0 56 126 140 146 150 170 206 240 276 296 300 306 320 390 446	-1010448403212
TPT(14)	2867952235076957471	0 2 48 50 78 80 198 200 300 302 378 380 420 422	-916981533258
SPT(16)	2867952364784708647	0 12 34 40 64 84 90 132 154 196 202 222 246 252 274 286	-787273782082
SPT(16)	2867952370125510859	0 28 42 48 60 64 78 114 148 184 198 202 214 220 234 262	-781932979870
TPT(14)	2867952573267591959	0 2 90 92 120 122 270 272 288 290 372 374 480 482	-578790898770
STPT(10)	2867953046641716989	0 2 48 50 90 92 132 134 180 182	-105416773740
TPT(14)	2867953749237801221	0 2 30 32 60 62 126 128 180 182 228 230 258 260	597179310492
SPT(16)	2867953976139621703	0 64 78 88 118 136 168 180 244 256 288 306 336 346 360 424	824081130974
SPT(16)	2867954044206605597	0 6 12 14 24 60 90 102 104 116 146 182 192 194 200 206	892148114868
STPT(10)	2867954287139936591	0 2 36 38 78 80 120 122 156 158	1135081445862
SPT(16)	2867954504202687629	0 48 134 158 218 224 230 248 294 312 318 324 384 408 494 542	1352144196900