; 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)