I’m not sure. I’d say it would depend on if you’ve got an actual procedure to do it. If yes, pretty close to 0. If not, maybe around 40 or so. Although the term “evolve” isn’t used, there are some procedures that try to do similar things.
Consider for example primitive roots. A primitive root an integer g such that g^k runs through every possible non-zero remainder when divided by p. Thus, for example, 2 is a primitive root modulo 5, since 2^1=2 (mod 5), 2^2=4 (mod 5), 2^3=8 = 3 (mod 5) and 2^4=16=1 (mod 5) so 1,2,3, and 4 are all accounted for. 2 is not a primitive root mod 7 since one only can get as remainders 1,2 and 4. (Most people here probbably already know about primitive roots but it seemed like a good idea to just go over the basics for readers who might know. Also my assumption that most people will know may be some form of projection and I’m assuming a much higher degree of knowledge about my field than can be reasonably expected). Now, it turns out that number theorists care a lot about primitive roots. Aside from intrinsic mathematical interest, they turn out to be useful in a number of practical algorithms such as the Diffie-Hellman algorithm which is a simple to implement key exchange procedure useful in cryptography.
It turns out that every prime has a primitive root (a non-obvious fact first proved by Gauss) but for a given prime, finding a primitive root is tough in general. However, some of the procedures used to find primitive roots work off of picking a set of random numbers, checking if any is a primitive root and if not combining them in a certain way to get a number whose powers run through more remainders. One can iterate this process to eventually get a primitive root. In some sense, this is evolving an answer to the problem, although that terminology would never be used. And there are procedures to find factors which rely on not so far off procedures (although calling them evolution would be more of a stretch). So the rough idea isn’t intrinsically crackpottish. It would depend a lot on the details.
I’m not sure. I’d say it would depend on if you’ve got an actual procedure to do it. If yes, pretty close to 0. If not, maybe around 40 or so. Although the term “evolve” isn’t used, there are some procedures that try to do similar things.
Consider for example primitive roots. A primitive root an integer g such that g^k runs through every possible non-zero remainder when divided by p. Thus, for example, 2 is a primitive root modulo 5, since 2^1=2 (mod 5), 2^2=4 (mod 5), 2^3=8 = 3 (mod 5) and 2^4=16=1 (mod 5) so 1,2,3, and 4 are all accounted for. 2 is not a primitive root mod 7 since one only can get as remainders 1,2 and 4. (Most people here probbably already know about primitive roots but it seemed like a good idea to just go over the basics for readers who might know. Also my assumption that most people will know may be some form of projection and I’m assuming a much higher degree of knowledge about my field than can be reasonably expected). Now, it turns out that number theorists care a lot about primitive roots. Aside from intrinsic mathematical interest, they turn out to be useful in a number of practical algorithms such as the Diffie-Hellman algorithm which is a simple to implement key exchange procedure useful in cryptography.
It turns out that every prime has a primitive root (a non-obvious fact first proved by Gauss) but for a given prime, finding a primitive root is tough in general. However, some of the procedures used to find primitive roots work off of picking a set of random numbers, checking if any is a primitive root and if not combining them in a certain way to get a number whose powers run through more remainders. One can iterate this process to eventually get a primitive root. In some sense, this is evolving an answer to the problem, although that terminology would never be used. And there are procedures to find factors which rely on not so far off procedures (although calling them evolution would be more of a stretch). So the rough idea isn’t intrinsically crackpottish. It would depend a lot on the details.