What data is saved in RSA private key?
You can print the data with (change PEM to DER if required):

openssl rsa -in Alice.key -text -inform PEM -noout

The following data is stored:


Modulus ($n = pq$)
Public exponent ($e$)
Private exponent ($d = e^{-1} \pmod{\phi{(n)}}$)
First prime ($p$)
Second prime ($q$)
First exponent, used for Chinese remainder theorem ($d_P = d \pmod{p - 1}$)
Second exponent, used for CRT ($d_Q = d \pmod{q - 1}$)
Coefficient, used for CRT ($q_{\mathrm{inv}} = q^{-1} \pmod{p}$)