Prime p₀= 2504789059619629229 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 4 2 142 2 16 2 10 2 (?)
a_n: 0 2 42 44 102 104 108 110 252 254 270 272 282 284
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: [AF>Linux]Rogue 9
db: batch=82, k=14, 40 58 4 142 16 10

SPT(16)	2504786875240144459	0 34 72 90 132 174 202 210 214 222 250 292 334 352 390 424	-2184379484770
STPT(10)	2504786993554551611	0 2 6 8 48 50 90 92 96 98	-2066065077618
SPT(16)	2504787092546390959	0 10 112 114 132 150 208 238 264 294 352 370 388 390 492 502	-1967073238270
SPT(16)	2504787678082954567	0 34 42 70 72 102 130 142 162 174 202 232 234 262 270 304	-1381536674662
SPT(16)	2504787687202934489	0 30 54 74 90 102 152 210 254 312 362 374 390 410 434 464	-1372416694740
TPT(14)	2504788623351339629	0 2 258 260 330 332 348 350 588 590 780 782 792 794	-436268289600
SPT(16)	2504789184308630627	0 72 80 116 134 144 162 246 290 374 392 402 420 456 464 536	124689001398
SPT(16)	2504789376359510623	0 40 54 160 174 190 208 220 318 330 348 364 378 484 498 538	316739881394
TPT(14)	2504789874472316987	0 2 162 164 210 212 252 254 342 344 372 374 444 446	814852687758
STPT(10)	2504790028764901697	0 2 30 32 42 44 54 56 84 86	969145272468
STPT(10)	2504790223718922989	0 2 12 14 90 92 168 170 180 182	1164099293760