n!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
| * 310: | \[310!!!+1\] | 146016469 × 514130808956383<15> × [96563923948781097703651097968718222646376815668972046104567522845539735895238669533134526955317880148132393488240875365751077181783553137650584347701400295141967604605540659735263848523062563<191>] |