Prime p₀= 249808786963112863 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 16 32 6 22 44 6 22 6 44 22 6 32 16 (?)
a_n: 0 16 48 54 76 120 126 148 154 198 220 226 258 274
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: 274
Found by: desktop64
db: batch=69, k=14, 16 32 6 22 44 6 22

SPT(14)	249808752631722659	0 12 30 50 60 110 114 140 144 194 204 224 242 254	-34331390204
SPT(14)	249808760167209577	0 6 22 34 90 112 120 136 144 166 222 234 250 256	-26795903286
SPT(14)	249808763954694157	0 16 22 42 64 76 82 114 120 132 154 174 180 196	-23008418706
SPT(14)	249808772617866437	0 20 24 96 104 110 126 134 150 156 164 236 240 260	-14345246426
SPT(14)	249808772697619453	0 16 40 70 90 96 108 226 238 244 264 294 318 334	-14265493410
SPT(14)	249808773417177673	0 4 66 96 154 156 180 184 208 210 268 298 360 364	-13545935190
SPT(14)	249808790463534041	0 20 42 50 62 78 108 122 152 168 180 188 210 230	3500421178
SPT(14)	249808804336700821	0 16 88 142 226 268 280 318 330 372 456 510 582 598	17373587958
SPT(14)	249808828504242373	0 36 78 150 160 168 174 190 196 204 214 286 328 364	41541129510
SPT(14)	249808829542423643	0 20 24 48 56 60 78 86 104 108 116 140 144 164	42579310780
SPT(14)	249808832001311549	0 18 30 50 84 128 158 204 234 278 312 332 344 362	45038198686