Prime p₀= 2089628173024516247 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 58 2 64 2 28 2 52 2 4 2 (?)
a_n: 0 2 54 56 114 116 180 182 210 212 264 266 270 272
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: 272
Found by: Conan
db: batch=80, k=14, 52 58 64 28 52 4

SPT(16)	2089627105926212791	0 52 66 78 102 162 186 198 220 232 256 316 340 352 366 418	-1067098303456
TPT(14)	2089627226628073157	0 2 42 44 54 56 114 116 174 176 180 182 210 212	-946396443090
SPT(16)	2089627319545060501	0 6 66 78 90 100 136 150 166 180 216 226 238 250 310 316	-853479455746
STPT(10)	2089627552724773379	0 2 48 50 90 92 132 134 180 182	-620299742868
SPT(16)	2089627734621530893	0 30 66 70 76 154 160 166 168 174 180 258 264 268 304 334	-438402985354
STPT(10)	2089628002900261247	0 2 30 32 72 74 114 116 144 146	-170124255000
SPT(16)	2089628498156108047	0 10 22 40 54 76 94 124 132 162 180 202 216 234 246 256	325131591800
SPT(16)	2089628583521358169	0 10 12 24 30 42 108 114 118 124 190 202 208 220 222 232	410496841922
SPT(16)	2089628741750374063	0 24 84 88 94 114 178 180 238 240 304 324 330 334 394 418	568725857816
SPT(16)	2089628828817228079	0 24 54 78 112 138 210 220 222 232 304 330 364 388 418 442	655792711832
SPT(18)	2089629407246350309	0 28 30 60 84 124 132 138 142 270 274 280 288 328 352 382 384 412	1234221834062