Here's an interesting question: will the program go faster if we replace all those
(n >) expressions with
(\x -> floor (sqrt n) > x)?
On one hand, a composite integer cannot possess a factor greater than its square root.
On the other hand, since the list we're looking through contains all possible prime numbers, we are guaranteed to find a factor or an exact match eventually, so do we need the
takeWhile at all?
Throwing this over to somebody with a bigger brain than me...
MathematicalOrchid 16:41, 5 February 2007 (UTC)
a composite can indeed have factors greater than its square root, and indeed most do. what you mean is that a composite will definitely have at least one factor smaller-equal than its square root.
why not use
(\x -> n > x*x) --Johannes Ahlmann 21:18, 5 February 2007 (UTC)
LOL! That is indeed what I meant.
It turns out my comment above is correct - the
takeWhile filtering in
factors is in fact unecessary. The function works just fine without it. (Notice I have made some edits to correct the multiple bugs in the
primes function. Oops!)
Now the only use of
takeWhile is in the
is_prime function, which could be changed to 'give up' the search a lot faster and hence confirm large primes with much less CPU time and RAM usage. Maybe I'll wrap my brain around that later.
MathematicalOrchid 10:17, 6 February 2007 (UTC)