n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 360: | \[360!!!!-1\] | 349 × 120149873 × 31092949272070972758781643<26> × [1746322092227882603457138076478168806263796732527510421710601562077881315209355498187459969642455250868809778898966050981098117679001309001772837223418032209<157>] |