Prime p₀= 521459319370397021 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 6 2 34 66 14 60 4 60 14 66 34 2 6 (?)
a_n: 0 6 8 42 108 122 182 186 246 260 326 360 362 368
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: 368
Found by: gemini8
db: batch=71, k=14, 6 2 34 66 14 60 4

SPT(14)	521459227975832863	0 10 48 66 70 90 124 150 184 204 208 226 264 274	-91394564158
SPT(16)	521459237008203343	0 6 16 48 54 100 156 166 168 178 234 280 286 318 328 334	-82362193678
SPT(16)	521459269761969479	0 54 72 162 182 252 254 360 362 468 470 540 560 650 668 722	-49608427542
SPT(14)	521459277744332339	0 32 44 98 150 158 170 222 234 242 294 348 360 392	-41626064682
STPT(10)	521459296127740589	0 2 48 50 90 92 132 134 180 182	-23242656432
TPT(12)	521459314327393859	0 2 18 20 30 32 72 74 102 104 138 140	-5043003162
TPT(12)	521459365844649017	0 2 30 32 84 86 90 92 102 104 144 146	46474251996
SPT(14)	521459430759831497	0 6 20 26 36 66 72 104 110 140 150 156 170 176	111389434476
SPT(22)	521459436777247621	0 6 60 66 168 178 190 196 226 240 288 310 358 372 402 408 420 430 532 538 592 598	117406850600
SPT(14)	521459440380614551	0 60 90 100 142 166 186 322 342 366 408 418 448 508	121010217530
TPT(12)	521459443092884477	0 2 30 32 42 44 54 56 150 152 252 254	123722487456