Prime p₀= 2522132922112408259 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 88 2 76 2 10 2 4 2 22 2 (?)
a_n: 0 2 42 44 132 134 210 212 222 224 228 230 252 254
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: 254
Found by: [AF>Linux]Rogue 9
db: batch=82, k=14, 40 88 76 10 4 22

SPT(16)	2522131269926070349	0 4 10 70 84 100 114 144 148 178 192 208 222 282 288 292	-1652186337910
SPT(16)	2522131547427317951	0 66 68 72 80 86 140 152 156 168 222 228 236 240 242 308	-1374685090308
SPT(16)	2522131880766556819	0 40 78 94 112 132 138 190 192 244 250 270 288 304 342 382	-1041345851440
STPT(10)	2522132466548065757	0 2 12 14 42 44 72 74 84 86	-455564342502
SPT(16)	2522132692425494573	0 24 60 138 140 150 164 228 230 294 308 318 320 398 434 458	-229686913686
STPT(10)	2522132721004482977	0 2 30 32 42 44 54 56 84 86	-201107925282
SPT(16)	2522133035761694903	0 14 18 20 44 146 170 204 350 384 408 510 534 536 540 554	113649286644
SPT(16)	2522133807922029221	0 32 50 68 78 110 188 198 242 252 330 362 372 390 408 440	885809620962
SPT(16)	2522134013042725673	0 30 48 56 78 98 138 204 230 296 336 356 378 386 404 434	1090930317414
TPT(14)	2522134071803410529	0 2 12 14 48 50 90 92 132 134 150 152 192 194	1149691002270
STPT(10)	2522134150701484349	0 2 18 20 30 32 42 44 60 62	1228589076090