Prime p₀= 281251643831996599 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 4 20 24 42 18 16 14 16 18 42 24 20 4 (?)
a_n: 0 4 24 48 90 108 124 138 154 172 214 238 258 262
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: 262
Found by: desktop64
db: batch=69, k=14, 4 20 24 42 18 16 14

SPT(14)	281251608553685173	0 24 34 48 60 136 178 186 228 304 316 330 340 364	-35278311426
SPT(14)	281251624485838673	0 8 18 24 36 44 80 84 120 128 140 146 156 164	-19346157926
SPT(14)	281251628029109383	0 16 46 48 90 100 120 154 174 184 226 228 258 274	-15802887216
SPT(14)	281251628813547901	0 6 10 60 66 112 130 132 150 196 202 252 256 262	-15018448698
TPT(12)	281251630837170737	0 2 42 44 72 74 84 86 120 122 132 134	-12994825862
TPT(12)	281251636187113619	0 2 18 20 30 32 60 62 150 152 198 200	-7644882980
SPT(14)	281251646560283149	0 28 60 70 72 90 100 102 112 130 132 142 174 202	2728286550
SPT(14)	281251652611963729	0 40 108 138 154 174 178 234 238 258 274 304 372 412	8779967130
TPT(12)	281251674972221099	0 2 12 14 42 44 108 110 150 152 282 284	31140224500
SPT(14)	281251692475386811	0 10 28 48 106 132 178 180 226 252 310 330 348 358	48643390212
SPT(14)	281251698968681803	0 10 70 88 94 120 124 150 154 180 186 204 264 274	55136685204