Prime p₀= 2539999789510986527 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 10 2 136 2 28 2 10 2 (?)
a_n: 0 2 60 62 90 92 102 104 240 242 270 272 282 284
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: [SG-2W]Kurzer
db: batch=82, k=14, 58 28 10 136 28 10

SPT(16)	2539997976355527223	0 6 18 28 40 76 90 100 186 196 210 246 258 268 280 286	-1813155459304
STPT(10)	2539998546175934027	0 2 30 32 60 62 90 92 120 122	-1243335052500
SPT(16)	2539998720576455923	0 4 58 70 100 144 210 220 354 364 430 474 504 516 570 574	-1068934530604
SPT(16)	2539998760229662931	0 12 26 36 80 132 140 146 156 162 170 222 266 276 290 302	-1029281323596
SPT(16)	2539998996937911469	0 28 64 72 88 120 130 184 198 252 262 294 310 318 354 382	-792573075058
STPT(10)	2539999760279586419	0 2 12 14 90 92 168 170 180 182	-29231400108
STPT(10)	2539999907601296477	0 2 30 32 42 44 54 56 84 86	118090309950
SPT(16)	2540000296832661251	0 50 56 66 110 138 182 206 252 276 320 348 392 402 408 458	507321674724
SPT(16)	2540000324915142539	0 42 60 62 90 98 104 134 168 198 204 212 240 242 260 302	535404156012
TPT(14)	2540000693180968727	0 2 24 26 90 92 150 152 162 164 180 182 222 224	903669982200
SPT(16)	2540000731918412911	0 42 78 130 210 228 232 252 256 276 280 298 378 430 466 508	942407426384