n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
318: | \[318!!!!!-1\] | 5 × 51991 × 563357 × 3031236889301<13> × 7930434763015282538057481042120104788919671679<46> × 2481200177170633983468705130576868170475944061106849533739585371<64> |