language: Scheme (guile) (guile 1.8.5)
date: 527 days 15 hours ago
link:
visibility: public 
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; http://programmingpraxis.com/contents/themes/#Prime Numbers
 
(define (expm b e m)
  (define (times p q) (modulo (* p q) m))
  (let loop ((b b) (e e) (x 1))
    (if (zero? e) x
      (loop (times b b) (quotient e 2)
            (if (odd? e) (times b x) x)))))
 
(define (primes n) ; assumes n is an integer greater than one
  (let* ((len (quotient (- n 1) 2)) (bits (make-vector len #t)))
    (let loop ((i 0) (p 3) (ps (list 2)))
      (cond ((< n (* p p))
              (do ((i i (+ i 1)) (p p (+ p 2))
                   (ps ps (if (vector-ref bits i) (cons p ps) ps)))
                  ((= i len) (reverse ps))))
            ((vector-ref bits i)
              (do ((j (+ (* 2 i i) (* 6 i) 3) (+ j p)))
                  ((<= len j) (loop (+ i 1) (+ p 2) (cons p ps)))
                (vector-set! bits j #f)))
            (else (loop (+ i 1) (+ p 2) ps))))))
 
(define prime? (let ((ps (primes 100)))
  (lambda (n) ; assumes n is an integer greater than one
    (define (spsp? n a)
      (define (f d s)
        (do ((r 0 (+ r 1)))
            ((or (= (expm a (* d (expt 2 r)) n) (- n 1)) (= r s))
              (< r s))))
      (do ((d (- n 1) (/ d 2)) (s 0 (+ s 1)))
          ((odd? d) (if (= (expm a d n) 1) #t (f d s)))))
    (if (member n ps) #t
      (do ((ps ps (cdr ps)))
          ((or (null? ps) (not (spsp? n (car ps)))) (null? ps)))))))
 
(define (factors n)
  (if (<= -1 n 1) (list n) (if (< n 0) (cons -1 (factors (- n)))
    (let fact ((n n) (c 1) (fs (list)))
      (define (f x) (modulo (+ (* x x) c) n))
      (if (even? n) (fact (/ n 2) c (cons 2 fs))
        (if (= n 1) fs (if (prime? n) (sort (cons n fs) <)
          (let loop ((t 2) (h 2) (d 1))
            (cond ((= d 1) (let ((t (f t)) (h (f (f h))))
                             (loop t h (gcd (- t h) n))))
                  ((= d n) (fact n (+ c 1) fs)) ; cyclic
                  ((prime? d) (fact (/ n d) (+ c 1) (cons d fs)))
                  (else (fact n (+ c 1) fs)))))))))))                 
 
(display (factors 41748850938502584251))