Prime p₀= 253165038616011827 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 12 42 20 30 36 12 22 12 36 30 20 42 12 (?)
a_n: 0 12 54 74 104 140 152 174 186 222 252 272 314 326
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: 326
Found by: desktop64
db: batch=69, k=14, 12 42 20 30 36 12 22

SPT(14)	253164997358387899	0 30 42 58 78 82 114 148 180 184 204 220 232 262	-41257623928
SPT(14)	253165005377009963	0 30 48 80 90 98 108 146 156 164 174 206 224 254	-33239001864
SPT(14)	253165009092290237	0 12 42 54 60 92 104 180 192 224 230 242 272 284	-29523721590
SPT(14)	253165019573865481	0 10 70 106 108 112 162 166 216 220 222 258 318 328	-19042146346
TPT(12)	253165021630123037	0 2 12 14 30 32 54 56 162 164 204 206	-16985888790
TPT(12)	253165028626409969	0 2 18 20 60 62 168 170 180 182 240 242	-9989601858
SPT(16)	253165039935685411	0 18 78 88 112 130 150 162 178 190 210 228 252 262 322 340	1319673584
SPT(14)	253165052679568219	0 40 42 72 82 94 112 150 168 180 190 220 222 262	14063556392
SPT(14)	253165058422179601	0 12 46 48 70 76 102 196 222 228 250 252 286 298	19806167774
SPT(14)	253165101486318199	0 34 58 118 168 178 198 304 324 334 384 444 468 502	62870306372
SPT(18)	253165121420823881	0 2 66 98 126 150 206 222 236 252 266 282 338 362 390 422 486 488	82804812054