section-1.2.6.rkt

#lang sicp

(define (expmod base exp m)
  (cond ((= exp 0) 1)
        ((even? exp)
         (remainder
           (square (expmod base (/ exp 2) m))
           m))
        (else
          (remainder
            (* base (expmod base (- exp 1) m))
            m))))

(define (expmod-v2 base exp m)
  (remainder (fast-expt base exp) m))

(define (fermat-test n)
  (define (try-it a)
    (= (expmod a n n) a))
  (try-it (+ 1 (random (- n 1)))))

(define (fermat-test-v2 n)
  (define (try-it a)
    (= (expmod-v2 a n n) a))
  (try-it (+ 1 (random (- n 1)))))

(define (fast-prime? n times)
  (cond ((= times 0) true)
        ((fermat-test n) (fast-prime? n (- times 1)))
        (else false)))

(define (fast-prime-v2? n times)
  (cond ((= times 0) true)
        ((fermat-test-v2 n) (fast-prime-v2? n (- times 1)))
        (else false)))

(define (fast-expt b n)
  (cond ((= n 0) 1)
        ((even? n) (square (fast-expt b (/ n 2))))
        (else (* b (fast-expt b (- n 1))))))

(define (smallest-divisor n)
  (find-divisor n 2))

(define (find-divisor n test-divisor)
  (cond
    ((> (square test-divisor) n) n)
    ((divides? test-divisor n) test-divisor)
    (else (find-divisor n (next test-divisor)))))

(define (divides? a b)
  (= (remainder b a) 0))

(define (square n)
  (* n n))

(define (prime? n)
  (= n (smallest-divisor n)))

(define (timed-prime-test n)
  (newline)
  (display n)
  (start-prime-test n (runtime)))

(define (start-prime-test n start-time)
  (if (fast-prime? n 5)
    (report-prime (- (runtime) start-time))))

(define (report-prime elapsed-time)
  (display " *** ")
  (display elapsed-time))

(define (search-for-primes start end)
  (cond
    ((> start end) (display "\ndone\n"))
    ((odd? start) (timed-prime-test start) (search-for-primes (+ start 2) end))
    (else (search-for-primes (+ start 1) end))))

(define (next n)
  (if (= n 2) 3 (+ n 2)))

; ex 1.25
; 
; It could, but it's significantly slower.