n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 340: | \[340!!!!-1\] | 6367 × 529048413712557371<18> × [125161827121012307071120031635793815886567744427609813798074852053118837892271442013873115649545925274505435698721374727547190566139696537124837048080596546707<159>] |