The challenge is: given a random private key, can you determine whether the key is greater than or less than this constant?
A private key is an integer and your constant is also an integer so you can perform a simple comparison to see which one is bigger. But if by "the key" you mean the "public key" then it is impossible because as it was mentioned the whole underlying cryptography would have been deemed broken and people would have been able to start solving the ECDLP!