Evolving Prime Number Algorithms: Can Computers Duplicate Human Programming?

[shivakumar06]

there are many prime number algorithm the simplest being dividing all the number less than the prime number. then comes division of number less than or equal half of the number to prime number with the prime number finally the division by all the smaller prime number than the given number with the required number. this is just the the way a program has evolved in the mind of the programmer. can this evolution of programming duplicated by the computer. if only the objective of programme given.(may be in haskell programming i am not sure) if yes by which programming language and the i need the key words that can be used as well

 

[NattyBumppo]

there are many prime number algorithm the simplest being dividing all the number less than the prime number. then comes division of number less than or equal half of the number to prime number

Actually, you only need to check possible primes up to the square root of the number you're trying to factor. Going up to half of the number you're trying to factor is overkill.

this is just the the way a program has evolved in the mind of the programmer. can this evolution of programming duplicated by the computer. if only the objective of programme given.(may be in haskell programming i am not sure) if yes by which programming language and the i need the key words that can be used as well

What you're talking about sounds like a cross between genetic programming and metaprogramming. There's been some work done in this area, such as meta-learning for machine learning algorithms, meta-genetic programming, and to a certain extent, machine learning in general. I recommend looking into these fields to start and seeing where that takes you.