Prime p₀= 1264415058579375653 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 14 4 122 6 22 20 42 34 42 20 22 6 122 4 14 (?)
a_n: 0 14 18 140 146 168 188 230 264 306 326 348 354 476 480 494
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 494
Found by: Megacruncher
db: batch=77, k=16, 14 4 122 6 22 20 42 34

SPT(16)	1264413735351443689	0 4 28 60 84 88 94 102 160 168 174 178 202 234 258 262	-1323227931964
SPT(16)	1264414455925701331	0 28 72 82 88 96 102 132 136 166 172 180 186 196 240 268	-602653674322
SPT(16)	1264414640272112519	0 42 54 78 180 192 218 224 348 354 380 392 494 518 530 572	-418307263134
SPT(16)	1264414702391225683	0 60 64 154 168 216 226 238 246 258 268 316 330 420 424 484	-356188149970
SPT(16)	1264414797872264461	0 12 16 40 42 90 142 156 166 180 232 280 282 306 310 322	-260707111192
STPT(10)	1264414947194186267	0 2 30 32 42 44 54 56 84 86	-111385189386
TPT(14)	1264415423084885681	0 2 108 110 120 122 150 152 198 200 210 212 408 410	364505510028
STPT(10)	1264415561621344577	0 2 30 32 42 44 54 56 84 86	503041968924
STPT(10)	1264416153180711239	0 2 42 44 60 62 78 80 120 122	1094601335586
SPT(18)	1264416527203746517	0 6 34 76 82 94 96 112 124 252 264 280 282 294 300 342 370 376	1468624370864
SPT(16)	1264416971532835411	0 22 42 90 100 120 148 162 166 180 208 228 238 286 306 328	1912953459758