; http://p...content-available-to-author-only...s.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))