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How to generate public/private keypair with RSA?

I'm developing several projects which use public/private key cryptography. So, the question is simple: how to generate public/private key pair?

As for me, I use OPENSSL to generate RSA key pair. It's simple:

openssl genrsa -out mykey.pem 2048

And public key can be generated like this:

openssl rsa -in mykey.pem -pubout > mykey.pub