# [plt-scheme] Comprehension: An example with five nested loops and four guards

 From: Jens Axel Søgaard (jensaxel at soegaard.net) Date: Mon Jun 4 14:47:43 EDT 2007 Previous message: [plt-scheme] Comprehension: An example with five nested loops and four guards Next message: [plt-scheme] Comprehension: An example with five nested loops and four guards Messages sorted by: [date] [thread] [subject] [author]

```David Einstein skrev:
> Does this give the set with the lowest sum?

Yes.

> Also, where is ec.ss?

Sorry I sent this to the wrong list. I didn't
mean to give away answers.

The version below includes prime?, next-prime
and :primes.

/Jens Axel

(require (planet "42.ss" ("soegaard" "srfi.plt")))

(define prime?
(let ()
; number of cached small primes
(define N 10000)

; n prime <=> (vector-ref primes n)
(define primes (make-vector N #t))

(vector-set! primes 0 #f)
(vector-set! primes 1 #f)

; sieve of Eratosthenes
(do-ec (:range n 2 N)
(if (vector-ref primes n))
(:range i (+ n n) N n)
(vector-set! primes i #f))

(lambda (n)
(cond
[(< n 0) #f]
[(< n N) (vector-ref primes n)]
[else    (let ([no-small-factor?
(every?-ec
(:let sqrt-n (integer-sqrt n))
(:while (:vector p-prime? (index p) primes)
(<= p sqrt-n))
(if p-prime?)
(not (zero? (remainder n p))))])
(and no-small-factor?
(or (< (sqrt n) N)
; large factors?
(every?-ec
(:let sqrt-n (+ (integer-sqrt n) 1))
(:range f (if (even? N) (+ N 1) N)
sqrt-n 2)
(not (zero? (remainder n f)))))))]))))

(define (next-prime n)
; find first prime larger than n
(cond
[(< n 2) 2]
[(= n 2) 3]
[(and (even? n) (not (prime? (+ n 1))))
(next-prime (+ n 1))]
[(even? n)
(+ n 1)]
[else
(first-ec 'never-used
; Chebyshev's Theorem says (* 2 n) okay
(:range m (+ n 2) (* 2 n) 2)
(if (prime? m))
m)]))

(define-syntax (:primes stx)
(syntax-case stx (index)
[(_ cc n (index i) . more)
#'(:parallel (:integers i) (_ n . more))]
[(_ cc n)
#'(:iterate n 2 next-prime (lambda (n) #f))]
[(_ cc n from)
#'(:iterate n from next-prime (lambda (n) #f))]
[(_ cc n from to)
#'(:iterate cc n from next-prime (let ([t to])
(lambda (n) (> n t))))]
[_
(raise-syntax-error
':primes
"expected (:primes from to), where from and to is optional"
stx)]))

(require mzscheme)

(define (number-append x y)
(string->number
(string-append
(number->string x) (number->string y))))
(define N 10000)

(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))

```

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