;; helpers

(define (sieve n)
  (define (aux u v)
    (let ((p (car v)))
      (if (> (* p p) n)
        (let rev-append ((u u) (v v))
          (if (null? u) v (rev-append (cdr u) (cons (car u) v))))
        (aux (cons p u)
          (let wheel ((u '()) (v (cdr v)) (a (* p p)))
            (cond ((null? v) (reverse u))
                  ((= (car v) a) (wheel u (cdr v) (+ a p)))
                  ((> (car v) a) (wheel u v (+ a p)))
                  (else (wheel (cons (car v) u) (cdr v) a))))))))
  (aux '(2)
    (let range ((v '()) (k (if (odd? n) n (- n 1))))
      (if (< k 3) v (range (cons k v) (- k 2))))))

(define (nth n l)
  (if (or (> n (length l)) (< n 0))
    (error "Index out of bounds.")
    (if (eq? n 0)
      (car l)
      (nth (- n 1) (cdr l)))))

;; e7

(nth 10000 (sieve 110000))