The key isn't generated from a username.

I managed to get the key validation routine, and it is rather complex.

I was able to translate it to Python code, and I tried generating random numbers and trying each generated number with the validating routine,

but I was not able to get a valid key, since the chance of each randomly generated number being valid is near 0.

What is the best way to generate a valid key?

you are going about it backwards.. what you are doing is no different than actually entering the number into the prog and clicking "check serial"

You need to follow each step of the validation routine to see what it is checking. search the authors site to see if you can find out what info the key is using to generate the key, if any. basically reverse the algorith. A bit hard to help anymore without more details.

the only way to get a valid key your current method is brute force, IE. check every number sequentially.