n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
171: | \[171!!!-1\] | 34583 × 1081079 × 15286602301140813982536251<26> × 2379044901768540028879953499<28> × 46797366164824303835272274317429045923943<41> |