n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
353: | \[353!!!!!+1\] | 4388801283623945673912016278728958430920911241708417889287812356444029180178391561928273804982055893617845648495341904865530322263045753325464554831873<151> |