Small correction: cryptographic algorithms don't depend on "prime numbers being hard to find", as they are not hard to find. Say you want to sample a 1024-bit prime. Then if you sample a random 1024-bit integer, it will be prime with probability 1/1024, roughly. This is a consequence of the prime number theorem [1]

Some crypto (namely, RSA) depends on on composite numbers being hard to factor, which is a different problem.

[1]: https://en.wikipedia.org/wiki/Prime_number_theorem