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    <p>Let us start by looking at the <code>divisors</code> function. It is sort of correct, with only two issues:</p> <ol> <li><p>What is the <code>xs</code> argument supposed to be? From the definition, it looks like it should be all the prime numbers below <code>x</code> - let's call these the candidate primes. So if <code>x</code> was <code>10</code>, then the candidate primes should be <code>[2,3,5,7]</code>. However, this is not what the function gets as an argument. In your code, <code>xs</code> is the infinite list of primes.</p></li> <li><p>Technically, the <code>divisors</code> doesn't return all divisors. <code>divisors 16 [2,3,5,7,11,13]</code> wouldn't return <code>8</code>, for instance. But this is a minor nitpick.</p></li> </ol> <p>So if we can call <code>divisors</code> with the right list of primes, then we should be ok, and the <code>isPrime</code> function would also be fine. </p> <p>The problem is getting the list of candidate primes. For clarity, I will give the code first, and then explain:</p> <pre><code>primeLst = 2 : [ x | x &lt;- [3..], isPrime x (takeWhile (\p -&gt; p*p &lt;= x) primeLst)] </code></pre> <p>I have made two changes:</p> <ol> <li><p>I made sure that <code>primeLst</code> includes <code>2</code>, by sticking it at the front. </p></li> <li><p>I restricted the candidate primes by taking numbers from the infinite list of primes until I reached a number that was higher than the square root of the number I was testing for primeness. In doing this i changed the definition of the candidate primes slightly, so for instance the candidates for <code>26</code> are <code>[2,3,5]</code> instead of <code>[2,3,5,7,11,13,17,19,23]</code>. But it still works.</p></li> </ol> <p>Two questions for you to think about: </p> <ol> <li><p>Why does it still work with the new definition of candidate primes?</p></li> <li><p>Why doesn't the following line of code work, even though it seems it should give the original definition of the candidate primes?</p></li> </ol> <p>:</p> <pre><code>primeLst = 2 : [ x | x &lt;- [3..], isPrime x (takeWhile (\p -&gt; p &lt; x) primeLst)] </code></pre> <p>The last question is hard, so if you have questions, post them in the comments.</p>
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    1. COThanks for your clarifications and time :D Haskell is an interesting programming language.. and here are my answer: 1. because haskell is lazy, it will take only numbers from primeLst that their square root is less than x without calculating paying attention to other list elements.. 2. because isPrime checks if the divisors are 1 and x and in this code x isn't there I think replacing `p < x` by `p <= x` may work.. Am I right?
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    2. COeuh.. there is an error.. `No instance for (Num [a0]) arising from a use of 'isPrime' Possible fix: add an instance declaration for (Num [a0]) In the expression: isPrime x (takeWhile (\ p -> p < x) primeLst) In a stmt of a list comprehension: isPrime x (takeWhile (\ p -> p < x) primeLst) In the second argument of '(:)', namely '[x | x <- [3 .. ], isPrime x (takeWhile (\ p -> p < x) primeLst)]'` what's wrong?
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    3. COHmm, I don't get the error. I have those three lines that you have in your question, with the `primeLst` definition as I wrote it. Are you sure you have exactly the same? With no type annotations. Did it work with the first definition of `primeLst` I wrote?
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