you (mostly) can't. In computing, "random" is a property of a process to generate a number, not a property of a number itself. You cannot directly analyze a number to determine it has been randomly generated.

There are some caveats here. There are some intrinsic properties of numbers that random numbers satisfy with high probability, e.g. having high kolmogorov complexity. But these are generally very difficult to compute, and I would personally guess you could concoct (probably artificial) scenarios where

1. picking parameters randomly yields a secure construction, but

2. there exists a parameter set with high kolmogorov complexity that is insecure.

e.g. "high kolmogorov complexity", while being a property of random numbers, is generally not viewed as nearly as useful as being randomly generated (which is exhibited by saying generator + seed = the particular number, like in this article).