This is the way, if FactorDB already knows a shorthand for that number:

- Take a number, let's say (287834098572304895723840598273045234-176435783429783541914131513478)/519589773265891366699777 (yes, some random dumb number) or this.
- The third column, "number", has the number displayed as link, followed by its factors as links. Click on the very first one, the one of the number itself.
- We get to this site. The search box now contains the known shorthand.
- Profit!

But I do not know how to tell FactorDB a new shorter formula for a given number.