n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
358: | \[358!!!!!-1\] | 52 × 569 × 653 × 121844807362428662563<21> × 205573721126438477959<21> × 3417999551237451959347<22> × 1975681182286300397034349435598007682675044008361884842378050540944926596146559423749<85> |