Do you mean the model # of the mower, or of the engine? Neither are 7 digits from what I can see.
The Simplicity: Stallion ZT2561 (a year 2002 model, i think), made by Ferris.
The Kohler: Model #CV25S, Spec #69557, Family: 2KHXS 7252GC
I tried the website you gave, but it does not accept my engine model #, which is the only model # on the engine label ... there's nothing more than that.
Also, in the "I don't know my model #, it does not list the "Command" series without the Pro ... my engine owner's manual does not say "Pro", so all I can conclude is that they have either dropped these older engines from their website, or the website never included them due to its newness. I tried the "Command Pro", but it didn't list my engine model.