n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
357: | \[357!!!!!-1\] | 5 × 1031 × 4421 × 294619861499<12> × 565172764149256889929<21> × 5595957179579011922797131467185696328728535240777<49> × 21118007919238541835007105739378104439328422668989408762338426131<65> |