https://ansuz.sooke.bc.ca/entry/23
tl;dr yes. An illegal number multiplied by two is illegal. Randomly generating that number is not. The illegality is not strictly a property of the number itself, but it's color.
https://ansuz.sooke.bc.ca/entry/23
tl;dr yes. An illegal number multiplied by two is illegal. Randomly generating that number is not. The illegality is not strictly a property of the number itself, but it's color.
Another idea is to generate a random number and multiply it with an illegal prime. If the illegal prime is a sufficiently large number; we can extract the original illegal prime with very high confidence by just finding its prime factors and picking the shortest one.
Therefore all numbers are illegal.
You can't just dodge color by mutating the number via mathematical operations, color doesn't work like that. You can only get rid of the taint by using a fresh number without taint.
If there's an illegal number X and I give you a number Y with the intention that you obtain X from it by some transform then Y is also illegal because I "tainted" it when I did the original transformation from X.
If I just need Y (or X) for some operation that's not related to the "illegality" then those numbers are not illegal.
The essay that droffel linked to explains this very well.
Two thoughts:
1. This appears to show a complete disregard for basic mathematics...
and
2. Do lawyers ever wonder why people make jokes about them?
The number itself isn't illegal, because it can come from any number of contexts. What's illegal is wilfully working towards generating that number while knowing its purpose as a key. It's just the principle of Mens Rea at work.