n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
257: | \[257!!!!!-1\] | 5 × 5237892702781<13> × 9792396424193<13> × 29341032813640539827573851485487749240359311983780646555502635096397747430959<77> |