n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
238: | \[238!!!!!-1\] | 5 × 707789 × 472407177659531<15> × 122265591791505094399<21> × 748074006496371780803191<24> × 41067441890843760805941591733<29> |