Project Euler 3

;;; Largest prime factor
;;; Problem 3
;;; The prime factors of 13195 are 5, 7, 13 and 29.
;;;
;;; What is the largest prime factor of the number 600851475143 ?
;;;
;;;

(defun prime-p (x)
  (cond ((eq 1 x) 1)
        ((eq 2 x) nil)
        ((eq 3 x) 3)
        (t (if (zerop (mod x 2)) nil
             (if (zerop (do ((half (floor (/ x 2)))
                             (n 2 (1+ n)))
                          ((or (zerop (mod x n)) (eq half n)) (mod x n))))
               nil x)))))

(defun find-factors (x)
  (loop for n from 1 to (sqrt x)
        if (zerop (mod x n))
          collect n into f-list
        finally (return f-list)))

(defun reduce-to-primes (lst)
  (remove-if #'(lambda (x) (if (not x) t nil)) (mapcar #'prime-p lst)))

(defun answer ()
  (reduce #'max (reduce-to-primes (find-factors 600851475143)))) ; 6857