[plt-scheme] Comprehension: An example with five nested loops and four guards
Does this give the set with the lowest sum?
Also, where is ec.ss?
On 6/4/07, Jens Axel Søgaard <jensaxel at soegaard.net> wrote:
>
> An "real world" example from Project Euler. It features
> five nested loops with four guards.
>
> The primes 3, 7, 109, and 673, are quite remarkable. By taking any
> two primes and concatenating them in any order the result will always
> be prime. For example, taking 7 and 109, both 7109 and 1097 are prime.
> The sum of these four primes, 792, represents the lowest sum for a
> set of four primes with this property.
>
> Find the lowest sum for a set of five primes for which any two primes
> concatenate to produce another prime.
>
>
> ; :primes ... and next-prime is in ec.ss.
> ; In prime? put an extra 0 or two on N, if you want
> ; more speed.
>
> (require ec mzscheme)
> (define N 10000)
>
> (define (number-append x y)
> (string->number
> (string-append
> (number->string x) (number->string y))))
>
>
> (first-ec 'not-found
> (:primes a 3 N)
> (:primes b (next-prime a) N)
> (if (and (prime? (number-append a b))
> (prime? (number-append b a))))
> (:primes c (next-prime b) N)
> (if (and (prime? (number-append a c))
> (prime? (number-append c a))
> (prime? (number-append b c))
> (prime? (number-append c b))))
> (:primes d (next-prime c) N)
> (if (and (prime? (number-append a d))
> (prime? (number-append d a))
> (prime? (number-append b d))
> (prime? (number-append d b))
> (prime? (number-append c d))
> (prime? (number-append d c))))
> (:primes e (next-prime d) N)
> (if (and (prime? (number-append a e))
> (prime? (number-append e a))
> (prime? (number-append b e))
> (prime? (number-append e b))
> (prime? (number-append c e))
> (prime? (number-append e c))
> (prime? (number-append d e))
> (prime? (number-append e d))))
> (list a b c d e))
>
>
>
>
> /Jens Axel
>
>
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