Prime p₀= 2357429815320593831 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 58 2 22 2 16 2 76 2 58 2 (?)
a_n: 0 2 96 98 156 158 180 182 198 200 276 278 336 338
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: 338
Found by: Donn Pike (USAF Ret)
db: batch=81, k=14, 94 58 22 16 76 58

SPT(16)	2357429344663561633	0 64 66 100 148 204 268 286 318 336 400 456 504 538 540 604	-470657032198
TPT(14)	2357429433950843867	0 2 30 32 192 194 222 224 240 242 264 266 294 296	-381369749964
STPT(10)	2357429495263042181	0 2 36 38 78 80 120 122 156 158	-320057551650
SPT(16)	2357429515671427163	0 14 24 80 84 98 116 128 156 168 186 200 204 260 270 284	-299649166668
TPT(14)	2357429644798629017	0 2 12 14 42 44 114 116 192 194 204 206 210 212	-170521964814
SPT(16)	2357429684844693847	0 22 36 40 82 124 142 150 196 204 222 264 306 310 324 346	-130475899984
STPT(10)	2357429846903046239	0 2 18 20 30 32 42 44 60 62	31582452408
SPT(16)	2357430140246330879	0 38 42 74 80 108 200 270 272 342 434 462 468 500 504 542	324925737048
SPT(16)	2357430310493076113	0 8 66 74 86 158 170 176 228 234 246 318 330 338 396 404	495172482282
STPT(10)	2357430339002868299	0 2 42 44 60 62 78 80 120 122	523682274468
SPT(16)	2357430496600722161	0 20 48 78 90 92 120 128 180 188 216 218 230 260 288 308	681280128330