project euler #3

(defvar *last-prime-factor* 2)
(setf *last-prime-factor* 2)

(defun prime-range (x n)
  (let ((n-sqrt (ceiling (sqrt n))))
    (cond ((or  (> x n-sqrt)) t)
          ((eq (rem n x) 0) nil)
          (t (prime-range (incf x) n)))))

(defun prime-num-p (x)
  (prime-range 2 x))

(defun int-p (x)
  (= (- x (floor x)) 0))

(defun lpf-inner (x n n-sqrt)
  (let* ((x-div (/ n x)))
    (cond ((or (eq n-sqrt x)
               (> x n-sqrt))
           *last-prime-factor*)
          ((and (eq (rem n x) 0)
                (prime-num-p x))
           (setf *last-prime-factor* x)
           (lpf-inner (incf x) n n-sqrt))
          ((and (int-p x-div)
                (> x-div x)
                (eq (rem n x-div) 0)
                (prime-num-p x-div))
           (setf *last-prime-factor* x-div)
           (lpf-inner (incf x) n n-sqrt))
          (t (lpf-inner (incf x) n n-sqrt)))))

(defun largest-prime-factor (n)
  (let* ((n-sqrt (ceiling (sqrt n))))
    (lpf-inner 2 n n-sqrt)))

(format t "~F~%" (largest-prime-factor 600851475143 ))