Prime p₀= 567540578699045311 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 6 22 24 14 24 6 16 6 24 14 24 22 6 (?)
a_n: 0 6 28 52 66 90 96 112 118 142 156 180 202 208
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: 208
Found by: gemini8
db: batch=71, k=14, 6 22 24 14 24 6 16

SPT(14)	567540458328241729	0 42 48 88 100 118 154 288 324 342 354 394 400 442	-120370803582
SPT(14)	567540519847167827	0 30 36 50 80 200 204 206 210 330 360 374 380 410	-58851877484
SPT(14)	567540526077169157	0 2 14 42 44 50 102 104 156 162 164 192 204 206	-52621876154
SPT(14)	567540526975788721	0 6 40 60 88 90 106 192 208 210 238 258 292 298	-51723256590
TPT(12)	567540552520603721	0 2 78 80 90 92 120 122 168 170 180 182	-26178441590
SPT(14)	567540552859746541	0 12 28 60 108 132 136 162 166 190 238 270 286 298	-25839298770
SPT(14)	567540583257557303	0 8 14 18 38 60 78 80 98 120 140 144 150 158	4558511992
SPT(14)	567540584001839779	0 22 24 64 84 88 114 148 174 178 198 238 240 262	5302794468
TPT(12)	567540594944513171	0 2 78 80 120 122 126 128 156 158 198 200	16245467860
TPT(12)	567540595946708687	0 2 90 92 114 116 120 122 132 134 144 146	17247663376
SPT(14)	567540611336172889	0 18 34 78 88 148 154 204 210 270 280 324 340 358	32637127578