If we can find prime numbers larger than 17 milion digits, why can't we find all 1024bit primes? "Largest Known Prime Number Discovered; Has 17,425,170 Digits"
http://www.sciencedaily.com/releases/2013/02/130213225424.htm

If we can find prime numbers larger than 17 milion digits,
why can't we find all 1024bit (just 309 decimal digits) primes?
Due to the prime number theorem the number of primes with length $2^{1024}$ is approximately

$$\pi(2^{1024}) - \pi(2^{1023})\approx  \frac{2^{1024}}{\ln(2^{1024})}- \frac{2^{1023}}{\ln(2^{1023})} \approx \frac{2^{{1024}}}{709.8} - \frac{2^{1023}}{709.1}\approx 2^{1013.5}$$

The number of atoms in the universe is approximately $10^{80} \approx 2^{265.75}$, which means...

Edit, fixing math:

... you would have to fit just around $2^{748} (\approx 2^{1013.5 - 265.75})$ prime numbers in every single atom in the universe in order to store this list.

To further break this down:
Assume you could program atoms to output 1 prime at a time for 1 attosecond (shortest measured time, $2^{-18}s$), you would still need $2^{663.1}$ years, and it's been "only" $2^{33.7}$ years since the Big Bang.

Short: It's far, far beyond the anything ever achievable. And this is not due to our technical limitations, it's just not possible in existence.