n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
317: | \[317!!!!-1\] | 25 × 789061055291<12> × 1396167756359183<16> × 30557710043557209943928689374958731621324699229371202240307523631996827810566596185309662296821731725957033855238152585229551241616278569<137> |