Some time ago, I did some research on the RSA algorithm because I learned some years ago that a private key cannot be extracted from a public key. As you know, web servers have certificates which all have a public key inside. So, what about the private key, are there any possibilities to get it ?
Well, it depends on the key generation process. I explain in my research paper on which way a private key can be recovered from a public key. In this vulnerability, I explain when two prime are generated during the key generation process are close to each other, the private key can easily be recovered.