n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 309: | \[309!!!!+1\] | 2 × 19526111837874163<17> × 953129440476499100014689949<27> × [291687450641287229357920782814948178779437475280505705041727935325880565960202211932970489356314302369440343851740249<117>] |