;;problem 3 largest prime factor of 600851475143

(defn prime? [x]
  (if (>= x 2)
    (zero?
     (count
      (filter #(divides? x %)
              (range 2 (inc (int (sqrt x)))))))
    false))

(defn get-biggest-prime-factor [x]
  (if (prime? x)
    x
    (let [lower-factors (filter #(zero? (rem x %))
                                (range 2 (inc (int (sqrt x)))))]
      (reduce max
              (concat
               (filter #(prime? %) lower-factors)
               (map #(/ x %) (filter #(prime? (/ x %)) lower-factors)))))))

(get-biggest-prime-factor 600851475143)