RSA public key of dead cryptographers
What you're looking for is hard-to-factor numbers where no one knows the factorization.

One approach to do this is to use the larger numbers in the RSA Factoring Challenge.  These are composite numbers selected by RSA Laboratories, in an attempt to encourage research on factorization methods.  As such, they went to great lengths to make sure that no one knew the factorization (including destroying the PC that generated the factors afterwards).

While the smaller numbers on the list have been factored, the larger ones (including RSA2048) have not.

I believe that this would address the problem you are attempting to solve.