project euler7 problem

;; Try the number against a list of all the previous primes
;; slow :(

(define primes (list 11 13 17 19 23 29)) ; the not-loop-unrolled primes
(define count (+ 4 (length primes)))

(define (is-prime? candidate)
  (define max (sqrt candidate))
  (define (loop-through pr)
    (cond
     [(> (car pr) max) #t]
     [(= 0 (remainder candidate (car pr))) #f]
     [else (loop-through (cdr pr))]))
  ;; first do some "loop unrolling"
  (cond
   [(= 0 (remainder candidate 3)) #f]
   [(= 0 (remainder candidate 5)) #f]
   [(= 0 (remainder candidate 7)) #f]
   [else (loop-through primes)]))


(define (get-10001st-prime)
  (let loop ([n 31])
    (cond
     [(is-prime? n)
      (if (= count 10001)
          n
          (begin
            (append! primes (list n))
            (set! count (+ 1 count))
            (loop (+ n 2))))]
     [else (loop (+ n 2))])))


; While this is a lot faster

(define (is-prime2? candidate)
  (define max (sqrt candidate))
  (let loop ([n 3])
    (cond
     [(> n max) #t]
     [(= 0 (remainder candidate n)) #f]
     [else (loop (+ n 2))])))

(define (get-10001st-prime2)
  (let loop ([i 5]
             [c 2])
    (if (is-prime2? i)
        (if (= c 10001)
            i
            (loop (+ i 2) (+ c 1)))
        (loop (+ i 2) c))))