How to convert a private key to an RSA private key?

This may be of some help (do not literally write out the backslashes '\' in the commands, they are meant to indicate that "everything has to be on one line"):

Which Command to Apply When

It seems that all the commands (in grey) take any type of key file (in green) as "in" argument. Which is nice.

Here are the commands again for easier copy-pasting:

openssl rsa                                                -in $FF -out $TF
openssl rsa -aes256                                        -in $FF -out $TF
openssl pkcs8 -topk8 -nocrypt                              -in $FF -out $TF
openssl pkcs8 -topk8 -v2 aes-256-cbc -v2prf hmacWithSHA256 -in $FF -out $TF

and

openssl rsa -check -in $FF
openssl rsa -text  -in $FF

Newer versions of OpenSSL say BEGIN PRIVATE KEY because they contain the private key + an OID that identifies the key type (this is known as PKCS8 format). To get the old style key (known as either PKCS1 or traditional OpenSSL format) you can do this:

openssl rsa -in server.key -out server_new.key

Alternately, if you have a PKCS1 key and want PKCS8:

openssl pkcs8 -topk8 -nocrypt -in privkey.pem