Semiprime numbers are natural numbers that are products of exactly two (possibly equal) prime numbers.


Semiprimes   are also known as:

   semi-primes
   biprimes
   bi-primes
    2-almost    primes
   or simply:    P2  


Example
 
   1679  =  23 × 73  

(This particular number was chosen as the length of the Arecibo message).



Task

Write a function determining whether a given number is semiprime.



See also

 The Wikipedia article:  semiprime.
 The Wikipedia article:  almost prime.
 The OEIS sequence:  A001358: semiprimes  which has a shorter definition: the product of two primes.


(defun semiprimep (n &optional (a 2))
  (cond ((> a (isqrt n)) nil)
        ((zerop (rem n a)) (and (primep a) (primep (/ n a))))
        (t (semiprimep n (+ a 1)))))
 
(defun primep (n &optional (a 2))
  (cond ((> a (isqrt n)) t)
        ((zerop (rem n a)) nil)
        (t (primep n (+ a 1)))))