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## Fun with guile, Erastones + goldbach conjecture

 From: Stefan Israelsson Tampe Subject: Fun with guile, Erastones + goldbach conjecture Date: Tue, 09 Apr 2013 00:03:11 +0200 User-agent: KMail/4.9.5 (Linux/3.5.0-26-generic; KDE/4.9.5; x86_64; ; )

```Hi all,

The program below is an interesting variant of a sieve that given an
even number seams to constructs two primes that added together becomes
the even
number, the file below does this construction for n = 3 ... 1000.

Have fun!

/Stefan

(use-modules (srfi srfi-1))

(define (analyze k)
(define n (* k 2))
(define l (apply circular-list (map (lambda (X) #f) (iota n))))
(define (shift l k)
(let loop ((l l) (k k))
(if (= k 0)
l
(loop (cdr l) (- k 1)))))

(define (next loop)
(let lp ((ll l) (i 0))
(if (= i n)
l
(if (car ll)
(lp (cdr ll) (+ i 1))
(loop i l 0)))))

(define (M)
(let lp ((l l) (k n) (M -1))
(if (= k 0)
M
(let ((c (caar l)))
(if (< M c)
(lp (cdr l) (- k 1) c)
(lp (cdr l) (- k 1) M))))))

(define (place x)
(let loop ((ll l) (i 0))
(if (equal? (car ll) x)
i
(loop (cdr ll) (+ i 1)))))

(set-car! (cdr l) (cons 1 0))
(set-car! (shift l (- n 1)) (cons 1 0))
(let loop ((m 2) (ll l) (k 0))
(let ((ll (shift ll m)))
(if (and (pair? (car ll)) (eq? (caar ll) m))
(next loop)
(begin
(unless (car ll) (set-car! ll (cons m k)) (set! k (+ k 1)))
(loop m ll k)))))

(let* ((M   (M))
(ll  (let lp ((ll l) (k n))
(if (= k 0)
'()
(cons (car ll) (lp (cdr ll) (- k 1))))))
(ll  (fold (lambda (k r)(if (eq? (car k) M) (cons k r) r)) '() ll))
(ll  (sort ll (lambda (x y) (< (cdr x) (cdr y))))))

(cond
((= (length ll) 1)
(* (place (car ll)) 2))
(else
(+ (place (car ll)) (place (car (last-pair ll))))))))

(let lp ((i 3))
(if (= i 1000)
(pk 'ok)
(begin
(if (not (= (* 2 i) (analyze i)))
(format #t "~a != (analyze ~a) == ~a~%" (* 2 i) (* 2 i)
(analyze (* 2i))))
(lp (+ i 1)))))
```

goldbach.scm
Description: Text Data