Prime p₀= 2953918908008741159 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 70 2 34 2 28 2 22 2 16 2 (?)
a_n: 0 2 60 62 132 134 168 170 198 200 222 224 240 242
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: 242
Found by: ginga
db: batch=82, k=14, 58 70 34 28 22 16

SPT(16)	2953915923774198529	0 12 28 54 60 112 142 172 180 210 240 292 298 324 340 352	-2984234542630
SPT(16)	2953916243235899761	0 10 30 78 88 102 156 166 252 262 316 330 340 388 408 418	-2664772841398
SPT(16)	2953916629018149551	0 26 30 32 42 72 122 180 308 366 416 446 456 458 462 488	-2278990591608
STPT(10)	2953916871596263667	0 2 54 56 132 134 210 212 264 266	-2036412477492
STPT(10)	2953918063535876189	0 2 18 20 30 32 42 44 60 62	-844472864970
STPT(10)	2953918298709722159	0 2 12 14 90 92 168 170 180 182	-609299019000
TPT(14)	2953918960899450149	0 2 60 62 90 92 258 260 270 272 282 284 342 344	52890708990
SPT(16)	2953919319817258909	0 34 48 72 88 160 174 202 240 268 282 354 370 394 408 442	411808517750
SPT(16)	2953919345925283013	0 50 56 104 134 150 158 204 230 276 284 300 330 378 384 434	437916541854
STPT(10)	2953919386473154751	0 2 36 38 78 80 120 122 156 158	478464413592
SPT(16)	2953920266173184879	0 42 98 104 110 114 120 132 140 152 158 162 168 174 230 272	1358164443720