primes in clojure

primes.clj

(ns primes)

(defn divides? [number divisor]
  (zero? (mod number divisor)))

(divides? 4 2) ;; => true
(divides? 8 1) ;; => true
(divides? 3 2) ;; => false
(divides? 2 4) ;; => false

(defn is-prime? [p]
  (let [possible-divisors (range 2 p)
        divides-p? (partial divides? p)]
    (not-any? divides-p? possible-divisors)))

(is-prime? 5) ;; => true
(is-prime? 9) ;; => false

;; counting primes in a range
(let [numbers (range 2 1000)]
  (-> (filter is-prime? numbers)
      count ;; remove/comment this line to see the numbers
      ))

(defn sieve [s]
  (cons (first s)
        (lazy-seq (sieve (remove #(zero? (mod % (first s))) s)))))

(take 100 (sieve (iterate inc 2))) ;; works fine, but 10000 explodes the stack

(defn not-divisable-by-any
  [number primes]
  (when (not-any? (partial divides? number) primes)
    number))

(defn next-prime [primes]
  (let [last-prime (last primes)
        next-possible (iterate inc (inc last-prime))]
    (->> (inc last-prime)
         (iterate inc)
         (some #(not-divisable-by-any % primes))
         (conj primes))))


(next-prime [2 3 5 7]) ;; [2 3 4 5 7 11]


(defn nth-prime [n]
  (last (last (take n (iterate next-prime [2])))))

(time (nth-prime 20000)) ;;