Goldbach function for list of even numbers [4..n]

Question

Hello I am trying to make a function goldbach :: Integer -> Bool for interval [4..n] that should return True only if all elements in that interval is even and can be summed from two prim numbers. So far I have done this.

goldbach::Integer->Bool
goldbach n 
    |goldbach2 n == ??? = goldbach (n-2)
    |n==4 = True
    |otherwise = False

goldbach2 :: Integer -> (Integer, Integer)
goldbach2 a = head $
                 filter (\(x,y) -> isPrime x && isPrime y) $
                 map (\e -> (e, a - e)) [3,5..a `div` 2]
where
factors a = filter (isFactor a) [2..a-1]
isFactor a b = a `mod` b == 0
isPrime a = null $ factors a

Function golbach2 result looks like this goldbac2 28 = (5, 23). How should I chek in my 3rd line goldbach2 n == ??? = goldbach (n-2) if result of goldbach2 n is correct and gives me two prim numbers?

Your description must be wrong, for, the only qualifying intervals are [] and `[4..4]` since in all the others there is at least one odd number. Hence, a short version of what you describe would be `g = (<=4)` — Ingo, Dec 04 '16 at 12:15
I don't get it how can that be. If I would enter `n=8` I should have a list `[4,6,8]` and it should return True. — Lukas Karmanovas, Dec 04 '16 at 12:27
Yes, you actually don't construct the interval `[4..n]` in your code. In the description, what you really mean is `[4,6 .. n]` — Ingo, Dec 04 '16 at 12:55

Paul Johnson · Accepted Answer · 2016-12-04T14:40:04.053

1

If I understand it correctly, you want something like:

 | let (n1, n2) = goldbach2 n in n == n1 + n2   =  goldbach (n-2)

edited Dec 04 '16 at 14:40

answered Dec 04 '16 at 11:50

Paul Johnson

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Yes I think that is something that I would need, but could you tell me how should I use it, I can't just simply replace my third line with yours or can I? – Lukas Karmanovas Dec 04 '16 at 12:07
I think you can, although I haven't tested it. The let ... in clause is the condition, and the single "=" is the value for that condition. Oh, and I forgot the leading "|". I'll edit that in. – Paul Johnson Dec 04 '16 at 14:29
Yeah but the problem is I am getting an error, that goldbatch is getting to few arguments – Lukas Karmanovas Dec 04 '16 at 14:35
Yeah never mind it just needed `n` after `goldbatch2` – Lukas Karmanovas Dec 04 '16 at 14:38

Ingo · Answer 2 · 2016-12-04T12:56:59.747

0

I would write this like

goldbachInterval n = all goldbach [4,6 .. n]
   where
       goldbach k = .... -- property of being a golbach number

edited Dec 04 '16 at 12:56

answered Dec 04 '16 at 12:22

Ingo

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Goldbach function for list of even numbers [4..n]

2 Answers2