n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
321: | \[321!!!!!+1\] | 458569 × 398029097125872068482819<24> × 944718659350887337110424126594692605393089366840017470882202351856976386504854598631800902296403371642707<105> |