Prime p₀= 2123349725390625617 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 118 2 34 2 40 2 16 2 82 2 (?)
a_n: 0 2 54 56 174 176 210 212 252 254 270 272 354 356
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: 356
Found by: Landjunge
db: batch=80, k=14, 52 118 34 40 16 82

TPT(14)	2123347933622369147	0 2 12 14 24 26 72 74 114 116 192 194 204 206	-1791768256470
SPT(16)	2123347975634471093	0 6 104 144 156 158 210 228 296 314 366 368 380 420 518 524	-1749756154524
SPT(16)	2123348050060817341	0 40 90 102 112 132 156 238 240 322 346 366 376 388 438 478	-1675329808276
SPT(16)	2123348074042029049	0 4 28 54 90 108 130 210 262 342 364 382 418 444 468 472	-1651348596568
TPT(14)	2123348217153059639	0 2 42 44 78 80 138 140 210 212 222 224 252 254	-1508237565978
STPT(10)	2123349441420310919	0 2 12 14 30 32 48 50 60 62	-283970314698
STPT(10)	2123349815983138607	0 2 12 14 72 74 132 134 144 146	90592512990
STPT(10)	2123349918048509327	0 2 60 62 72 74 84 86 144 146	192657883710
SPT(16)	2123350107215709553	0 34 54 60 90 130 150 174 220 244 264 304 334 340 360 394	381825083936
SPT(16)	2123350129152087371	0 18 20 60 72 86 138 152 246 260 312 326 338 378 380 398	403761461754
TPT(14)	2123350394596585211	0 2 30 32 66 68 126 128 156 158 168 170 276 278	669205959594