Prime p₀= 2956373512555907681 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 112 2 178 2 34 2 22 2 16 2 (?)
a_n: 0 2 66 68 180 182 360 362 396 398 420 422 438 440
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: 440
Found by: Landjunge
db: batch=82, k=14, 64 112 178 34 22 16

STPT(10)	2956371849861336587	0 2 90 92 102 104 114 116 204 206	-1662694571094
SPT(16)	2956371977256240919	0 24 70 120 150 154 204 234 304 334 384 388 418 468 514 538	-1535299666762
SPT(16)	2956372989540176207	0 96 150 152 176 212 240 266 276 302 330 366 390 392 446 542	-523015731474
STPT(10)	2956373240157491837	0 2 12 14 72 74 132 134 144 146	-272398415844
STPT(10)	2956373251176245429	0 2 42 44 90 92 138 140 180 182	-261379662252
SPT(16)	2956373393762134891	0 30 58 72 76 90 100 142 186 228 238 252 256 270 298 328	-118793772790
SPT(16)	2956373563703034749	0 14 50 134 150 158 164 180 182 198 204 212 228 312 348 362	51147127068
SPT(16)	2956373568665846969	0 8 14 92 104 164 168 198 224 254 258 318 330 408 414 422	56109939288
SPT(16)	2956373604364379357	0 2 6 12 26 32 42 56 90 104 114 120 134 140 144 146	91808471676
STPT(10)	2956373671202018057	0 2 12 14 42 44 72 74 84 86	158646110376
SPT(16)	2956373823203480023	0 4 10 36 126 154 186 204 220 238 270 298 388 414 420 424	310647572342