Prime p₀= 2623711254653585867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 286 2 16 2 208 2 10 2 (?)
a_n: 0 2 24 26 84 86 372 374 390 392 600 602 612 614
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: 614
Found by: RFGuy_KCCO
db: batch=82, k=14, 22 58 286 16 208 10

SPT(16)	2623709966581845787	0 6 24 34 84 106 126 216 220 310 330 352 402 412 430 436	-1288071740080
SPT(16)	2623710136057425749	0 24 48 68 122 138 182 222 230 270 314 330 384 404 428 452	-1118596160118
STPT(10)	2623710226889991047	0 2 12 14 72 74 132 134 144 146	-1027763594820
SPT(16)	2623710511970396963	0 8 20 50 56 156 168 170 174 176 188 288 294 324 336 344	-742683188904
SPT(16)	2623710690457229213	0 60 78 98 120 158 164 170 234 240 246 284 306 326 344 404	-564196356654
STPT(10)	2623711154100752039	0 2 18 20 30 32 42 44 60 62	-100552833828
SPT(16)	2623711526910853727	0 6 32 90 102 150 192 200 402 410 452 500 512 570 596 602	272257267860
SPT(16)	2623711677101721203	0 20 60 78 86 98 126 138 176 188 216 228 236 254 294 314	422448135336
STPT(10)	2623711826402445197	0 2 42 44 72 74 102 104 144 146	571748859330
SPT(16)	2623711900204319707	0 6 34 46 70 72 76 124 132 180 184 186 210 222 250 256	645550733840
SPT(16)	2623712230829860763	0 68 98 108 110 120 134 138 176 180 194 204 206 216 246 314	976176274896