Lisp中的质数检查

Question

Can someone point out my mistake here. I am trying to check if a number is a prime number or not. It works to an extent but I have a semantics error. For example it is telling me that 9 is a prime number but at the same time it is telling me 4 and 6 are not prime numbers and I am confused.

(defvar *prime* nil)

(defun primeCheck (x y)
    (if (and (>= x y) (not (= (mod x y) 0))) 
        (progn 
            (setf y (+ y 1))
            (primeCheck x y)
            (setf *prime* 'yes))
    (setf *prime* 'no))
)
(primeCheck 9 2)
(if  (equal *prime* 'yes) (print "Number is prime") (print "Number is not prime"))

Answer 1

I suggest you to download some IDE (for example LispWorks Personal Edition) or find online REPL for Common Lisp and run your codes in it. Your mistakes:

• ("prime number") is badly formed list. Replace that with (print "prime number")
• primeCheck calls some (yet) undefined function modulus
• (*prime-Check* nil) is badly formed list. Replace with (setf *prime-Check* nil)
• badly formed cond and and
• with all these corrections, it doesn't work for 2,3,5 etc.

Answer 2

Many things are wrong.

How about using primarity test eg from SICP (structure and interpretation of computer programs)?

;; from SICP (here in clojure)
;; http://www.sicpdistilled.com/section/1.2.6/

(defun smallest-divisor (n)
  (find-divisor n 2))

(defun square (n)
  (* n n))

(defun find-divisor (n test-divisor)
  (cond ((> (square test-divisor) n) n)
        ((dividesp test-divisor n) test-divisor)
        (t (find-divisor n (1+ test-divisor)))))

(defun dividesp (a b)
  (zerop (mod b a)))

(defun primep (n)
  (= n (smallest-divisor n)))

primep tests for primarity.