Prime p₀= 2301726980682766319 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 4 2 28 2 10 2 76 2 40 2 (?)
a_n: 0 2 12 14 18 20 48 50 60 62 138 140 180 182
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: 182
Found by: Landjunge
db: batch=81, k=14, 10 4 28 10 76 40

SPT(16)	2301725237849510677	0 12 64 70 102 142 156 180 196 220 234 274 306 312 364 376	-1742833255642
TPT(14)	2301725651052465719	0 2 12 14 102 104 132 134 180 182 408 410 420 422	-1329630300600
SPT(16)	2301726353519391551	0 30 90 102 110 180 200 216 236 252 272 342 350 362 422 452	-627163374768
SPT(16)	2301726357561700943	0 14 30 60 74 86 98 108 146 156 168 180 194 224 240 254	-623121065376
SPT(16)	2301726765858409991	0 56 98 110 132 150 168 188 210 230 248 266 288 300 342 398	-214824356328
SPT(16)	2301726940215586607	0 6 20 54 140 152 174 176 180 182 204 216 302 336 350 356	-40467179712
STPT(10)	2301727007370662759	0 2 18 20 30 32 42 44 60 62	26687896440
SPT(16)	2301727198123166483	0 26 36 54 66 68 108 140 174 206 246 248 260 278 288 314	217440400164
SPT(16)	2301727914599827969	0 30 34 48 54 84 114 154 168 208 238 268 274 288 292 322	933917061650
SPT(16)	2301729022373781421	0 22 40 42 66 78 88 100 108 120 130 142 166 168 186 208	2041691015102
STPT(10)	2301729359783797079	0 2 42 44 90 92 138 140 180 182	2379101030760