n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
217: | \[217!!!!-1\] | 22 × 70474414911097073291566003<26> × 104069406324493415454416611<27> × 7658984771164037117856542573127064442209383432752657<52> |