Prime p₀= 404016029867800943 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 14 6 18 16 14 66 16 66 14 16 18 6 14 (?)
a_n: 0 14 20 38 54 68 134 150 216 230 246 264 270 284
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: 284
Found by: Cruncher Pete
db: batch=70, k=14, 14 6 18 16 14 66 16

SPT(14)	404015972048049967	0 12 16 60 90 100 124 132 156 166 196 240 244 256	-57819750976
TPT(12)	404015976540218771	0 2 120 122 126 128 150 152 210 212 276 278	-53327582172
TPT(12)	404015981814991457	0 2 30 32 60 62 114 116 132 134 174 176	-48052809486
SPT(16)	404015999175495803	0 18 26 50 56 78 98 158 228 288 308 330 336 360 368 386	-30692305140
SPT(14)	404016004489984721	0 8 30 38 80 132 156 182 206 258 300 308 330 338	-25377816222
SPT(14)	404016027341331473	0 8 14 48 90 126 144 260 278 314 356 390 396 404	-2526469470
SPT(14)	404016082892440027	0 34 60 66 76 120 154 192 226 270 280 286 312 346	53024639084
TPT(12)	404016113074791197	0 2 12 14 24 26 54 56 162 164 180 182	83206990254
SPT(14)	404016135930285751	0 52 126 190 208 210 222 286 298 300 318 382 456 508	106062484808
TPT(12)	404016184656536057	0 2 90 92 114 116 210 212 240 242 270 272	154788735114
TPT(12)	404016223576889351	0 2 30 32 36 38 96 98 138 140 180 182	193709088408