Shall we embrace I discovered (I do know, unimaginable) public key elements.
Bitcoin public keys are coordinates of issues at the secp256k1 elliptic curve. They don’t seem to be integers, and thus factoring isn’t an operation that applies to them.
What to do with them subsequent to compute unique personal key for that public key?
Bitcoin’s (ECDSA) safety is in line with the hardness of computing the discrete logarithm of issues at the secp256k1 curve, now not at the problem of factoring huge integers (like e.g. the RSA set of rules is). Gaining access to a quick integer factorization set of rules is not going to in anyway can help you compute personal keys of Bitcoin public keys briefly.