n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
240: | \[240!!!!!-1\] | 107 × 258581 × 3562367310949<13> × 243867825442021188329<21> × 30832076183552882923331<23> × 59510367856244620964650181966447<32> |