Reviewing the SSH keys of hosts that I connect to (as gathered by PuTTY in registry key HKEY_CURRENT_USER\SoftWare\SimonTatham\PuTTY\SshHostKeys), I find that they all start with 0x10001 (65537) or 0x23 (35), most often followed by 2048-bit composite values with no small factor. I conclude they are RSA keys, and that 0x23 (35) is the second most common public exponent in my sampling.
What software commonly generates RSA keys with that public exponent 0x23 (35)? Why that value, which is not prime, and thus slightly complicates the selection of the factors of the public modulus?