n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
240: | \[240!!!!+1\] | 61 × 809 × 25849 × 292787344061<12> × 32184998052331600174199<23> × 920124169206208673566660349597614518873169420955178686875986940802386768559<75> |