Prime p₀= 2687956682721303779 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 34 2 52 2 124 2 22 2 (?)
a_n: 0 2 30 32 42 44 78 80 132 134 258 260 282 284
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: JayPi
db: batch=82, k=14, 28 10 34 52 124 22

SPT(16)	2687954830840745273	0 8 20 38 86 90 108 210 254 356 374 378 426 444 456 464	-1851880558506
SPT(16)	2687955117499263701	0 12 42 68 92 102 110 168 200 258 266 276 300 326 356 368	-1565222040078
SPT(16)	2687955160225385383	0 6 46 84 156 186 204 216 268 280 298 328 400 438 478 484	-1522495918396
SPT(16)	2687955838056058469	0 30 48 54 78 138 180 204 258 282 324 384 408 414 432 462	-844665245310
STPT(10)	2687956064475953039	0 2 18 20 30 32 42 44 60 62	-618245350740
SPT(16)	2687956550826219851	0 8 36 38 48 50 66 78 98 110 126 128 138 140 168 176	-131895083928
SPT(16)	2687956803563875637	0 84 92 156 216 282 302 320 366 384 404 470 530 594 602 686	120842571858
STPT(10)	2687957234503496237	0 2 42 44 72 74 102 104 144 146	551782192458
STPT(10)	2687957613961530731	0 2 6 8 18 20 30 32 36 38	931240226952
STPT(10)	2687957639099304287	0 2 42 44 72 74 102 104 144 146	956378000508
STPT(10)	2687957849793816539	0 2 18 20 60 62 102 104 120 122	1167072512760