; generating large random primes (define rand (let ((seed 0.3141592654)) (lambda args (set! seed (if (pair? args) (sin (car args)) (let ((x (* seed 147.0))) (- x (floor x))))) seed))) (define (randint first past) (inexact->exact (floor (+ (* (- past first) (rand)) first)))) (define (primes n) ; list of primes not exceeding n (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? ; strong pseudoprime to prime bases less than 100 (let* ((ps (primes 100)) (p100 (apply * ps))) (lambda (n) (define (expm b e m) (let loop ((b b) (e e) (x 1)) (if (zero? e) x (loop (modulo (* b b) m) (quotient e 2) (if (odd? e) (modulo (* b x) m) x))))) (define (spsp? n a) ; #t if n is a strong pseudoprime base a (do ((d (- n 1) (/ d 2)) (s 0 (+ s 1))) ((odd? d) (if (= (expm a d n) 1) #t (do ((r 0 (+ r 1))) ((or (= (expm a (* d (expt 2 r)) n) (- n 1)) (= r s)) (< r s))))))) (if (< n 2) #f (if (< 1 (gcd n p100)) (if (member n ps) #t #f) (do ((ps ps (cdr ps))) ((or (null? ps) (not (spsp? n (car ps)))) (null? ps)))))))) (define sievers (primes (expt 2 16))) (define (rand-prime lo hi) (define (rand-odd lo hi) (let ((n (randint lo hi))) (if (odd? n) n (+ n 1)))) (let outer-loop ((base (rand-odd lo (- hi 100000)))) (let ((sieve (make-vector 50000 #t))) (do ((ps (cdr sievers) (cdr ps))) ((null? ps)) (let ((p (car ps))) (do ((i (modulo (* -1/2 (+ base p)) p) (+ i p))) ((<= 50000 i))))) (let inner-loop ((i 0)) (if (<= 50000 i) (outer-loop (rand-odd lo (- hi 100000))) (if (and (vector-ref sieve i) (prime? (+ base i i))) (+ base i i) (inner-loop (+ i 1)))))))) (display (rand-prime #e1e49 #e1e50)) (newline)