Prime p₀= 316752465173950679 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 20 10 8 36 100 14 22 14 100 36 8 10 20 (?)
a_n: 0 20 30 38 74 174 188 210 224 324 360 368 378 398
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: 398
Found by: desktop64
db: batch=70, k=14, 20 10 8 36 100 14 22

SPT(14)	316752401906478079	0 12 24 40 64 70 120 124 174 180 204 220 232 244	-63267472600
SPT(14)	316752415405950521	0 26 30 60 96 116 152 216 252 272 308 338 342 368	-49768000158
SPT(14)	316752441061939249	0 28 48 70 78 82 180 232 330 334 342 364 384 412	-24112011430
SPT(14)	316752451579853299	0 28 52 84 168 174 190 252 268 274 358 390 414 442	-13594097380
SPT(14)	316752461493320911	0 10 22 36 48 78 88 90 100 130 142 156 168 178	-3680629768
SPT(14)	316752462056916629	0 8 24 74 78 104 150 182 228 254 258 308 324 332	-3117034050
SPT(14)	316752490697101471	0 18 48 60 70 136 148 150 162 228 238 250 280 298	25523150792
SPT(14)	316752493207927717	0 30 40 54 64 90 96 100 106 132 142 156 166 196	28033977038
SPT(14)	316752495576504167	0 14 116 122 164 182 192 284 294 312 354 360 462 476	30402553488
SPT(14)	316752498995034457	0 24 76 82 102 160 172 174 186 244 264 270 322 346	33821083778
SPT(14)	316752510391401151	0 28 42 46 96 172 196 222 246 322 372 376 390 418	45217450472