n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
253: | \[253!!!!-1\] | 27 × 5777720751135121<16> × 3245202445494858677<19> × 218975223284385005131574122084532963158777477252980956330496516138151428508621601605983749<90> |