Prime p₀= 4588261635766316821 starts a Symmetric tuple of 22 consecutive primes (SPT).
d_n: 0 82 14 16 24 44 30 18 10 12 6 86 6 12 10 18 30 44 24 16 14 82 (?)
a_n: 0 82 96 112 136 180 210 228 238 250 256 342 348 360 370 388 418 462 486 502 516 598
All 22 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 598
Found by: Stony666
db: batch=85, k=22, 82 14 16 24 44 30 18 10 12 6 86

STPT(10)	4588260418498830431	0 2 66 68 138 140 210 212 276 278	-1217267486390
SPT(16)	4588260450872267699	0 14 60 74 80 132 138 144 188 194 200 252 258 272 318 332	-1184894049122
SPT(16)	4588260899598920267	0 14 36 86 140 146 176 194 276 294 324 330 384 434 456 470	-736167396554
STPT(10)	4588261086436499909	0 2 48 50 90 92 132 134 180 182	-549329816912
TPT(14)	4588261172607966857	0 2 84 86 150 152 174 176 252 254 264 266 390 392	-463158349964
SPT(16)	4588261182318863327	0 12 54 56 92 110 134 152 204 222 246 264 300 302 344 356	-453447453494
SPT(16)	4588261849452592859	0 42 48 60 72 84 104 114 188 198 218 230 242 254 260 302	213686276038
SPT(16)	4588261895561715997	0 22 40 72 94 132 156 220 306 370 394 432 454 486 504 526	259795399176
SPT(16)	4588261903927662559	0 4 34 60 70 78 84 100 132 148 154 162 172 198 228 232	268161345738
SPT(16)	4588262131625423327	0 30 114 126 150 152 194 212 264 282 324 326 350 362 446 476	495859106506
STPT(12)	4588262294781025697	0 2 42 44 72 74 102 104 132 134 174 176	659014708876