Prime p₀= 2567358623340779381 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 130 2 76 2 70 2 88 2 40 2 (?)
a_n: 0 2 36 38 168 170 246 248 318 320 408 410 450 452
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: 452
Found by: SEARCHER
db: batch=82, k=14, 34 130 76 70 88 40

SPT(16)	2567357693674629907	0 6 84 106 120 160 184 210 316 342 366 406 420 442 520 526	-929666149474
SPT(16)	2567357770306682279	0 14 42 62 78 104 110 132 170 192 198 224 240 260 288 302	-853034097102
SPT(16)	2567357800132342901	0 50 60 80 92 110 138 140 228 230 258 276 288 308 318 368	-823208436480
STPT(10)	2567357942220161861	0 2 78 80 138 140 198 200 276 278	-681120617520
SPT(16)	2567358016881180857	0 6 36 50 54 92 122 266 300 444 474 512 516 530 560 566	-606459598524
SPT(16)	2567358176424060863	0 50 54 60 84 96 120 156 158 194 218 230 254 260 264 314	-446916718518
TPT(14)	2567358698323566989	0 2 78 80 90 92 210 212 252 254 270 272 282 284	74982787608
SPT(16)	2567359145419071271	0 28 72 126 142 160 190 220 258 288 318 336 352 406 450 478	522078291890
TPT(14)	2567359364493111047	0 2 144 146 222 224 234 236 252 254 264 266 354 356	741152331666
TPT(14)	2567359572557440931	0 2 6 8 18 20 138 140 156 158 210 212 228 230	949216661550
TPT(14)	2567359804736651711	0 2 66 68 78 80 96 98 120 122 138 140 180 182	1181395872330