Prime p₀= 279020110626217957 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 24 12 40 8 10 32 58 32 10 8 40 12 24 (?)
a_n: 0 24 36 76 84 94 126 184 216 226 234 274 286 310
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: 310
Found by: Ralfy
db: batch=69, k=14, 24 12 40 8 10 32 58

SPT(14)	279020042094025963	0 24 34 64 90 100 120 154 174 184 210 240 250 274	-68532191994
SPT(14)	279020044778819081	0 2 8 30 36 38 96 122 180 182 188 210 216 218	-65847398876
SPT(14)	279020060878585681	0 18 40 72 78 156 162 166 172 250 256 288 310 328	-49747632276
SPT(14)	279020071558196473	0 4 40 46 120 138 186 208 256 274 348 354 390 394	-39068021484
TPT(12)	279020087813290667	0 2 30 32 54 56 180 182 240 242 264 266	-22812927290
SPT(14)	279020094098902081	0 90 102 126 142 172 186 286 300 330 346 370 382 472	-16527315876
TPT(12)	279020122658120687	0 2 54 56 240 242 264 266 270 272 282 284	12031902730
SPT(14)	279020123814470537	0 2 30 32 42 44 72 74 102 104 114 116 144 146	13188252580
TPT(14)	279020123814470537	0 2 30 32 42 44 72 74 102 104 114 116 144 146	13188252580
STPT(14)	279020123814470537	0 2 30 32 42 44 72 74 102 104 114 116 144 146	13188252580
SPT(14)	279020138959503299	0 2 12 78 114 144 164 198 218 248 284 350 360 362	28333285342