How to create a public and private key pair for RSA encryption

gistfile1.txt

# 1. Generate a new RSA key pair (public and private key) with a 4096 bit long modulus.
# You can optionally pass e.g. '-aes256' to encrypt the key pair with a passphrase. The key
# pair will be saved as 'private.pem' ('pem' is just a container file format,
# see https://serverfault.com/questions/9708/what-is-a-pem-file-and-how-does-it-differ-from-other-openssl-generated-key-file).
openssl genrsa -out private.pem 4096

# 2. Extract the public key from the RSA key pair ('private.pem').
# The result is again saved in a 'pem' file, this time named 'public.pem'. 
openssl rsa -in private.pem -outform PEM -pubout -out public.pem

# 3. Verify the contents of the two files
# private.pem: should start with '-----BEGIN RSA PRIVATE KEY-----' in its first line
head private.pem
# public.pem: should start with '-----BEGIN PUBLIC KEY-----' in its first line
head public.pem