n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 331: | \[331!!!!!+1\] | 5783 × 2543999822279<13> × [1264728577970706576167259808438675553495645576152293661677416244306159567711348549905934908604864640049982446916455509648801<124>] |