n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
| * 477: | \[477!!!!!+1\] | 66277177073<11> × 1045019924761<13> × 14843044942736689579<20> × [354471168205216766691802370944417262661058280048315743303423317384483581036545298276046550683753801643415336127208613419141903192601872124709554960761524926540607983824580651<174>] |