Msieve & Yafu - RSA Exponents and bruteforcing
The fact that public exponent $e$ is $17$ does not help. The standard attack against RSA keys generated correctly (except for the small size of their public modulus $N$) is to factor $N$. That's the only input of the factoring task, which is where overwhelmingly most of the effort goes.

$e$ is involved only in preparing the final form of the private key, which is easy: the code to prepare the private key from $e$ and prime factors $p$, $q$ of $N$ is in anything that generates an RSA key in the desired format. For the  $N(n,d)$ format, a working $d$ is $e^{-1}\bmod((p-1)(q-1))$ and that's a one-liner in Python: d=pow(17,-1,(p-1)*(q-1)).

At 512-bit, GNFS is the algorithm of choice and the two usual bottlenecks are sieving and the matrix step. Multiple CPUs definitely help for sieving. For the matrix step, it's complicated, but a machine with large memory is required.

Have a look at CADO-NFS for an implementation.

It is disputed if GPUs are useful at factoring, and I have yet to find any account of actual use at 512-bit.

If you have multiple $N$ with some generated by a defective process, there might be special attacks computing the GCD for pairs of $(N_i,N_j)$, $i&lt;j$. When one is found that is not $1$, that trivially factors $N_i$ and $N_j$. It's worth trying if the "long-shutdown videogame" was using a poor key generator, even more so in a CTF context. There are improvements to this, both computational and to extend the class of exploitable weak generators; see this.