Cracking RSA — A Challenge Generator

Do you have what it takes to be a cipher cracker? Well here is a challenge for you [here]:

RSA Encryption parameters. Public key: [e,N].
e: 65537
N: 498702132445864856509611776937010471
Cipher: 96708304500902540927682601709667939
We are using 60 bit primes
Can you find the value of the message?

With this we are using the RSA encryption method, and we have the encryption key (e,N). We must find the two prime numbers which create the value of N (p and q), and must use a factorization program to find them. Once we find the factors it is easy to then determine the decryption key (d,N).

Example

Here is an example:

Encryption parameters
e:	65537
N:	1034776851837418228051242693253376923
Cipher:	582984697800119976959378162843817868
We are using  60 bit primes

Now we have to crack N by finding the primes that make up the value.

If we use this [link], we get:

Factors
-------
1,034,776,851,837,418,228,051,242,693,253,376,923 = 1,086,027,579,223,696,553 x 952,809,000,096,560,291

p=1,086,027,579,223,696,553 q=952,809,000,096,560,291

Now we work out PHI, which is equal to (p−1)×(q−1):

>>>p=1086027579223696553…