# 99 questions/31 to 41

### From HaskellWiki

Line 8: | Line 8: | ||

== Problem 31 == |
== Problem 31 == |
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− | <Problem description> |
+ | Determine whether a given integer number is prime. |

<pre> |
<pre> |
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Example: |
Example: |
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− | <example in lisp> |
+ | * (is-prime 7) |

+ | T |
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Example in Haskell: |
Example in Haskell: |
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− | <example in Haskell> |
+ | P31> isPrime 7 |

+ | True |
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</pre> |
</pre> |
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Solution: |
Solution: |
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<haskell> |
<haskell> |
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− | <solution in haskell> |
+ | isPrime :: Integral a => a -> Bool |

+ | isPrime p = all (\n -> p `mod` n /= 0 ) $ takeWhile (\n -> n*n <= x) [2..] |
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</haskell> |
</haskell> |
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− | <description of implementation> |
+ | Well, a natural number p is a prime number iff no natural number n with n >= 2 and n^2 <= p is a divisor of p. That's exactly what is implemented: we take the list of all integral numbers starting with 2 as long as their square is at most p and check that for all these n there is a remainder concerning the division of p by n. |

== Problem 32 == |
== Problem 32 == |

## Revision as of 19:00, 12 December 2006

These are Haskell translations of Ninety Nine Lisp Problems.

If you want to work on one of these, put your name in the block so we know someone's working on it. Then, change n in your block to the appropriate problem number, and fill in the <Problem description>,<example in lisp>,<example in Haskell>,<solution in haskell> and <description of implementation> fields.

## 1 Problem 31

Determine whether a given integer number is prime.

Example: * (is-prime 7) T Example in Haskell: P31> isPrime 7 True

Solution:

isPrime :: Integral a => a -> Bool isPrime p = all (\n -> p `mod` n /= 0 ) $ takeWhile (\n -> n*n <= x) [2..]

Well, a natural number p is a prime number iff no natural number n with n >= 2 and n^2 <= p is a divisor of p. That's exactly what is implemented: we take the list of all integral numbers starting with 2 as long as their square is at most p and check that for all these n there is a remainder concerning the division of p by n.

## 2 Problem 32

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 3 Problem 33

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 4 Problem 34

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 5 Problem 35

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 6 Problem 36

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 7 Problem 37

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 8 Problem 38

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 9 Problem 39

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>

## 10 Problem 40

<Problem description>

Example: <example in lisp> Example in Haskell: <example in Haskell>

Solution:

<solution in haskell>

<description of implementation>