Verifiable random number

I need to generate a large set of 10 digit random numbers. The number has to be verifiable in some way that this it was generated by this system. I could thik of some approaches which I describe below

Approach 1: Add some parts of this random number with values that are part of the system internals, example, IP, MAC address, timestamp, hashvalue of customer & others.

This reduces the randomness due to some static/lesser dynamic parts occupying the random number. However, anyone who knows this pattern can generate a number, unless the value is not internal.

Approach 2: Mod-97 10 Attach the digest to this number so that it is verifiable. However, this, I believe, can also be generated by anyone who knows there is digest attached to every random number. Am I right?

Approach 3: Generate the digest including a secret key that is part of the system. Unless someone knows the secret key, they cannot create a random number with a digest.

Have any of you solved this in a different way? Would be glad if you could point be to a direction to this solution, or give me an answer itself.

Cheers