(defn square [n]
  (* n n))

(defn even? [n]
  (= (mod n 2) 0))

(defn expmod [base exp m]
  (defn squaring-test [k]
    (cond
      (and
        (not (= k 1))
        (not (= k (- m 1)))
        (= (mod (square k) m) 1)) 0
      (mod (square k) m)))
  (cond
    (= exp 0) 1
    (even? exp) (squaring-test (expmod base (/ exp 2) m))
    (mod (* base (expmod base (- exp 1) m)) m)))

(defn miller-rabin-test [n]
  (defn random [n]
    (math/floor (* (math/random) n)))
  (defn try-it [a]
    (def test (expmod a (- n 1) n))
    (cond
      (= test 0) false
      true))
  (try-it (+ 1 (random (- n 1)))))

(defn prime? [n times]
  (cond
    (= times 0) true
    (miller-rabin-test n) (prime? n (- times 1))
    false))


(print "Should be true")
(print (prime? 11 100))
(print (prime? 13 100))
(print (prime? 5 100))

(print "Should be false")
(print (prime? 561 100))
(print (prime? 1105 100))
(print (prime? 1729 100))
(print (prime? 2465 100))
(print (prime? 2821 100))
(print (prime? 6601 100))