Euler Project 47

The first two consecutive numbers to have two distinct prime factors are:

14 = 2  7
15 = 3  5

The first three consecutive numbers to have three distinct prime factors are:

644 = 2²  7  23
645 = 3  5  43
646 = 2  17  19.

Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers?

My Solution

(defun factorlist(num)

  (loop for i from 2 to (floor (sqrt num))

          when(zerop (rem num i))

          collect i

          when(zerop (rem num i))

          collect (/ num i)))

(defun  primep (n)

        (cond ((minusp n) 'nil)

                  ((= 2 n) t)

                 ((evenp n) 'nil)

                 ((= 1 n) 'nil)

                 (t (let ((limit (floor (sqrt n))))

                      (do ((i 3 (incf i 2)))

                            ((> i limit) t)

                            (if (= 0 (mod n i)) (return-from primep 'nil)))))))

(defun FourePrimeFactors(l)

      (length (remove-if-not #'primep l)))

(defun Euler47(n)

  (loop for i from 100000 to n

         do(if (and (= 4 (FourePrimeFactors (factorlist i)))

                          (= 4 (FourePrimeFactors (factorlist (+ i 1))))

                          (= 4 (FourePrimeFactors (factorlist (+ i 2))))

                          (= 4 (FourePrimeFactors (factorlist (+ i 3)))))

     (return i))))