Prime p₀= 2868997667608533887 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 28 2 28 2 286 2 16 2 58 2 (?)
a_n: 0 2 54 56 84 86 114 116 402 404 420 422 480 482
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: 482
Found by: Landjunge
db: batch=82, k=14, 52 28 28 286 16 58

STPT(10)	2868996753840116951	0 2 6 8 18 20 30 32 36 38	-913768416936
SPT(16)	2868996831868539529	0 100 108 120 174 180 208 210 232 234 262 268 322 334 342 442	-835739994358
STPT(10)	2868997197685700759	0 2 18 20 30 32 42 44 60 62	-469922833128
STPT(10)	2868997425798642107	0 2 54 56 72 74 90 92 144 146	-241809891780
STPT(10)	2868997508122956149	0 2 42 44 60 62 78 80 120 122	-159485577738
STPT(10)	2868997643013310967	0 2 30 32 72 74 114 116 144 146	-24595222920
SPT(16)	2868997861385090131	0 12 22 42 48 58 60 120 208 268 270 280 286 306 316 328	193776556244
SPT(16)	2868997972670230657	0 6 34 100 106 114 126 180 226 280 292 300 306 372 400 406	305061696770
SPT(16)	2868998011976930423	0 20 38 90 98 104 188 198 326 336 420 426 434 486 504 524	344368396536
SPT(16)	2868998328469645621	0 36 60 96 130 132 162 196 222 256 286 288 322 358 382 418	660861111734
SPT(16)	2868998692299631141	0 46 60 82 108 136 150 172 186 208 222 250 276 298 312 358	1024691097254