n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 517: | \[517!!!!!+1\] | 11775089 × 141616250188981<15> × [845054803557298301191654094631689262531052177659834962560389251753185940284394959914528280655594778886439770747023284015010547757230143315383277398415509815958835954363265720007850804340788484824056688076305802593773<216>] |