n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
| 367: | \[367!!!!!+1\] | 5 × 283 × 2251 × 2437 × 7333 × 751027 × 1052119 × 92269109 × 26925362744487458459274757<26> × 533196074510992466784632316231652092019964027645493912394164836939063586835945929385451247058015537<99> |