Prime number estimation

non-estimate.clj

(defn prime? [x]
  (let [divs (range 2 (inc (int (Math/sqrt x))))
        rems (map #(rem x %) divs)]
    (not (some zero? rems))))

(filter prime? (range 1000))

prime.clj

(defn expmod
  "calculates (base**exp) % m"
  [base exp m]
  (letfn [(sq [x] (* x x))]
    (cond
      (= exp 0) 1
      (even? exp) (rem (sq (expmod base (/ exp 2) m)) m)
      :else (rem (* base (expmod base (- exp 1) m)) m))))

(defn fermat-test [n]
  (letfn [(try [a](= (expmod a n n) a))]
    (try (+ 1 (rand-int (- n 1))))))

(defn prime? [n times]
  (cond
    (= times 0) true
    (fermat-test n) (prime? n (- times 1))
    :else false))

(->> (iterate inc 1) (drop-while #(< % 1000)) (filter #(prime? % 5)) (take 100))