n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 348: | \[348!!!!!+1\] | 52 × 1496773689079672655249791<25> × [332257706474645583482423658131394065492520642713920096166239441700785389578717993050357821636585830428741614363255493305943<123>] |