Prime p₀= 2736584721693395891 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 28 2 28 2 22 2 34 2 10 2 (?)
a_n: 0 2 6 8 36 38 66 68 90 92 126 128 138 140
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: 140
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 4 28 28 22 34 10

SPT(16)	2736582367149844217	0 30 72 140 156 162 176 222 344 390 404 410 426 494 536 566	-2354543551674
STPT(10)	2736582526556180189	0 2 18 20 30 32 42 44 60 62	-2195137215702
SPT(18)	2736582963326569963	0 34 36 64 78 166 168 190 210 244 264 286 288 376 390 418 420 454	-1758366825928
SPT(16)	2736583786910297437	0 16 36 40 66 70 120 142 204 226 276 280 306 310 330 346	-934783098454
SPT(16)	2736584001986778061	0 70 96 100 112 132 166 172 210 216 250 270 282 286 312 382	-719706617830
STPT(10)	2736584590727117027	0 2 42 44 102 104 162 164 204 206	-130966278864
SPT(16)	2736585064715626549	0 40 84 132 154 162 178 192 220 234 250 258 280 328 372 412	343022230658
STPT(10)	2736585111690650159	0 2 30 32 60 62 90 92 120 122	389997254268
SPT(16)	2736585665661305917	0 16 60 130 166 184 196 214 222 240 252 270 306 376 420 436	943967910026
SPT(16)	2736585668068561307	0 20 36 50 74 84 116 204 206 294 326 336 360 374 390 410	946375165416
SPT(16)	2736585852794002259	0 42 84 110 122 134 150 152 222 224 240 252 264 290 332 374	1131100606368