n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 358: | \[358!!!!!+1\] | 66463 × 8358869131<10> × 316645896951616290661<21> × [8931566018106785715398665127894811424168692672610651458184841568060659023772009337674090518721719703258728710945488569<118>] |