RSA is not used to encrypt large messages. Symmetric ciphers are used for this. With classic RSA, the secret key for the symmetric cipher is encrypted using RSA

RSA is not used to encrypt large messages. Symmetric ciphers are used for this. With classic RSA, the secret key for the symmetric cipher is encrypted using RSA. Often (e.g. in the Signal protocol), a short secret key is extended using a HKDF (RFC 5869) to create enough bits for a symmetric key and an IV or a nonce (and a MAC key if needed). So for randomness, take 128 bits, use HKDF to extend to 192 bits, use 128 bits of output as AES-128 key, use next 64 bits of output as nonce, use 64 bits counter, produce AES-128(key, nonce||counter) for every value of counter until it overflows as randomness. 2^64 of 2^4 byte blocks is 2^68 bytes of randomness - enough for most purposes. An Intel chip will produce it at 1GB/sec per core.