n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
221: | \[221!!!!-1\] | 24 × 9431 × 14601752740789139719919<23> × 539041804738494544608379<24> × 22562159999885229097846169<26> × 1853071544525230452269742115501<31> |