n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 347: | \[347!!!!+1\] | 24 × 1709 × 2141 × 45781903529<11> × [5026158043946411565815938964519277222957760696020344475917852363094356629416964154277119992969558545423017126897854388165980810357269524047811333185883485511625551111<166>] |