I'm not sure your math checks out. With 1024 bits of entropy and, say, 1 trillion valid links, your chances of any one link being valid are 1/2^984

So test a million links - your probability of finding a real one is (1-1/2^984)^1000000. That's around 1/10^291 chance of hitting a valid URL with a million tries. Even if you avoid ever checking the same URL twice it will still take you an impractical amount of time.