Prime p₀= 567540263311192519 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 18 4 18 42 20 42 4 42 20 42 18 4 18 (?)
a_n: 0 18 22 40 82 102 144 148 190 210 252 270 274 292
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: 292
Found by: gemini8
db: batch=71, k=14, 18 4 18 42 20 42 4

SPT(16)	567540190026031531	0 12 46 70 82 102 108 112 126 130 136 156 168 192 226 238	-73285160988
SPT(14)	567540204708989059	0 22 48 70 88 118 130 132 144 174 192 214 240 262	-58602203460
SPT(14)	567540236073605293	0 24 30 66 76 88 90 154 156 168 178 214 220 244	-27237587226
SPT(14)	567540244903985569	0 24 30 54 58 84 90 118 124 150 154 178 184 208	-18407206950
SPT(14)	567540245763976297	0 54 60 66 96 150 154 252 256 310 340 346 352 406	-17547216222
SPT(14)	567540246046296499	0 22 40 82 124 130 144 148 162 168 210 252 270 292	-17264896020
SPT(14)	567540302321844697	0 4 52 54 60 70 82 102 114 124 130 132 180 184	39010652178
SPT(14)	567540308241387757	0 24 70 84 94 112 132 202 222 240 250 264 310 334	44930195238
SPT(14)	567540331317710669	0 50 72 78 98 102 158 174 230 234 254 260 282 332	68006518150
SPT(14)	567540332166445199	0 14 30 38 48 90 104 168 182 224 234 242 258 272	68855252680
SPT(14)	567540345484251311	0 2 32 42 50 56 90 98 132 138 146 156 186 188	82173058792