When people go searching for prime numbers / bitcoin with massive compute, I assume that there are huge libraries of "shortcuts" to reduce the searching space, like prime numbers only appear with certain patterns, or there are large "holes" in the number space that do not need to be searched, etc. (see videos e.g. about how prime numbers make spirals on the polar coord. system, etc). I.e. if you know these you can accelerate/reduce your search cost by orders of magnitude.
For whatever various encryption algorithm that people choose to test or attack (like this story), is there somewhere such libraries of "shortcuts" are kept and well known? To reduce the brute force search need?
And is the state of sharing these to the point that the encryption services are designed to avoid the shortcut vulnerabilities?
Was always wondering this.