how to evaluate if this (or any) bitcoin public key / private key combination is valid? Let's say some software gave me the following combination:

public key:

13YcHBzsBX8SxHoBftb69cXJkdXLfAVQos


private key:

KwfNqMip1ZdgG2o6wYQUBXv8BqkMQ8VWWeScVU5TLPZp31M5EHeq


And let's say that for whatever reason, I want to test the validity:


that the public key is a valid bitcoin address that can receive payments, and
that the private key is valid for this particular public key


What are my options to evaluate the validity of 1 and 2?
1) A Bitcoin address is between 25 and 34 characters long

2) the address always starts with a 1 (in this case)

3) an address can contain all alphanumeric characters, with the exceptions of 0, O, I, and l.

(ref: https://thomas.vanhoutte.be/tools/validate-bitcoin-address.php)

Now here comes the hard part: The last four bytes of the address are the first four bytes of Sha256(Sha256(2,3,4...21th bytes of the address))

More info: https://bitcoin.stackexchange.com/a/50879/38618