n!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
153: | \[153!!!+1\] | 55683913 × 84795166987877<14> × 443046781311100943<18> × 2006804311691395301<19> × 795744383503118363209420163177807<33> |