I just realized that the word for organ the music instrument and the body part is one and the same in English. (In dutch they're called orgel and orgaan respectively.) Which of these meanings is being referred to in the article? To me both could make sense.
The definition of organ in this article is closest to the body part definition. The use of organ here relies on a less common definition: roughly a constituent part of some larger whole that performs a specific function.
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.
For other cryptographic operations, almost any sufficiently large prime can be used. Even a 50% reduction on a computation that will take trillions of years, has no practical impact.