n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
288: | \[288!!!!!+1\] | 5 × 1931 × 7442532233<10> × 27387295044945216538707761517598855991<38> × 5472549749055878003527358710480630476464667312925821723812433522409<67> |