n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 667: | \[667!!!!!-1\] | 491 × 1459 × 4027 × 15883289 × 4916640222421<13> × [968508522145509433223839744335370608197660357037765783677474707297943241135933370046841172320443781261337048114577965288601638483872266270477791747551706940929390364160414867767841965555823518150502335892723469024948388895285846065451424847679859994424265915474679427091488307986781657664369<291>] |