Let p be a natural number for which there exist two natural numbers s.t.

p = nm + n + m = (n+1)(m+1) - 1 ==> p - 1 = (n+1)(m+1).

If every natural number p can be obtained, then since every natural number can be written as p-1 we get that every natural number can be expressed as (n+1)(m+1)...but there are infinite very easy to find natural numbers that can NOT be expressed this way...

Tonio