You don't generate the shared prime number or the generator for Diffie-Hellman. See:
http://en.wikipedia.org/wiki/Diffie-Hellman_key_exchange
The parameters P and G are agreed to ahead of time by both sides. Using the notation of the Wikipedia article, crypto:dh_generate_key is used for steps 2 & 3 to generate a / A & b / B , and then crypto:dh_compute_key is used for steps 4 & 5 to compute the shared secret s .
For RSA , I don't know of a standard library function that generates a public/private key pair. Generating primes is a fairly involved algorithm from what I remember; I would strongly recommend you not try to code it yourself. Diffie-Hellman key pairs are not suitable for use with RSA; they are different algorithms intended for different purposes.
Generally you don't need to generate these at runtime since you can reuse the key pair. You can use any number of other sources to actually generate it. (Maybe ssh-keygen would work? And there's always OpenSSL .) To use the key pair you've created, you'd use the crypto:rsa_ public/private _ encrypt/decrypt functions.

See cutkey ( https://github.com/yrashk/cutkey )
"cutkey is an Erlang app for generating RSA keys. It is implemented as a port driver that calls OpenSSL's RSA_generate_key on a thread from the async pool."

操作系统：命令（“openssl genpkey -算法RSA -输出私钥。pem -pkeyopt rsa密钥生成位：2048”）。

You can use the crypto:generate_key/2 function to create RSA public and private keys:
For a 2048 length

{Pub, Priv} = crypto:generate_key(rsa, {2048,65537}).

Or for a 1024 length

{Pub, Priv} = crypto:generate_key(rsa, {1024,65537}).

See: https://erlang.org/doc/apps/crypto/crypto.pdf (page 37)

generate_key(Type, Params) -> {PublicKey, PrivKeyOut}

Where

Type = rsa

Params = rsa_params() =
    {ModulusSizeInBits :: integer(),
     PublicExponent :: key_integer()}