n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
316: | \[316!!!!!-1\] | 5 × 317 × 349919 × 835427 × 3094974616999<13> × 279605273606371<15> × 1339705149454321010466071113995276767680648735106956798949450228598511461415311965781622319<91> |