n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
321: | \[321!!!!-1\] | 25 × 228220393314659<15> × 142812777597355628173<21> × 331552674561682707940923759766597302493707362216786203536836175188213937485497129482203504708967933876482290960497212291325998185601<132> |