n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
244: | \[244!!!!!+1\] | 53 × 106649 × 21350291 × 804907397044427<15> × 18570905072112699602195954979342636634463049892420623587971084280653<68> |