Prime p₀= 2869065980475563591 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 40 2 136 2 28 2 10 2 (?)
a_n: 0 2 30 32 48 50 90 92 228 230 258 260 270 272
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: Landjunge
db: batch=82, k=14, 28 16 40 136 28 10

SPT(16)	2869064690464674803	0 6 36 50 54 78 96 156 188 248 266 290 294 308 338 344	-1290010888788
STPT(10)	2869064705964137477	0 2 24 26 42 44 60 62 84 86	-1274511426114
SPT(16)	2869065015512268871	0 58 72 78 102 112 138 172 198 232 258 268 292 298 312 370	-964963294720
SPT(16)	2869065023248453927	0 36 66 100 126 130 172 190 192 210 252 256 282 316 346 382	-957227109664
STPT(10)	2869065544110371687	0 2 54 56 132 134 210 212 264 266	-436365191904
STPT(10)	2869065614169366329	0 2 12 14 90 92 168 170 180 182	-366306197262
SPT(16)	2869066263928072067	0 12 32 44 90 104 132 140 186 194 222 236 282 294 314 326	283452508476
SPT(20)	2869066354907034769	0 22 40 42 90 102 130 142 148 180 232 264 270 282 310 322 370 372 390 412	374431471178
SPT(16)	2869067144468982559	0 40 70 112 130 138 154 172 180 198 214 222 240 282 312 352	1163993418968
TPT(14)	2869067435651052989	0 2 108 110 132 134 138 140 168 170 192 194 210 212	1455175489398
TPT(14)	2869067599418799017	0 2 54 56 72 74 114 116 180 182 192 194 204 206	1618943235426