An 2048 bit RSA key has 112 bits of security, but not necessarily 2048 bits of entropy. RSA 2048 only has about ~112 bits of security because there are faster-t

An 2048 bit RSA key has 112 bits of security, but not necessarily 2048 bits of entropy. RSA 2048 only has about ~112 bits of security because there are faster-than-brute-force algorithms for integer factorization. A 2048 bit RSA key is generated from two 1024 bit primes. Let's assume we randomly choose each prime from the range 2^1023 to 2^1024. Per the Prime Number Theorem, there are ~ N / ln (N) primes below N. That means that there are 2^1024 / (1024 ln 2) - 2^1023 / (1023 ln 2) ≈ 1.3e305 1024-bit primes. It follows that a 1024 bit prime has ~1023 bits of entropy and that a 2048 bit RSA key has ~2022 bits of entropy.