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RSA public key and private key calculation: multiple answer
Given N = 91
public key (11, 91)
Ciphertext = 88 ^11 mod 91 = 30
30 ^ 59 mod 91 = 88 (plaintext)
30 ^ 11 mod 91 = 88 (plaintext)
30 ^ 47 mod 91 = 88 (plaintext)
How can there be multiple suitable instance of private key such as 59/11/47?
Lastly, must public and private key always be a prime number?