Demonstrates the Goldbach's conjecture - Every even integer greater than 2 can be expressed as the sum of two primes

goldbach.lisp

;*******************************************************************************************************************
;Demonstrates the Goldbach's conjecture - Every even integer greater than 2 can be expressed as the sum of two primes
;
;Author: Igor Hercowitz
;
;usage: clisp goldbach.lisp <number>
;output: the sum of the primes list
;
;Ex: 
;> clisp goldbach.lisp 100
;97 + 3 95 + 5 91 + 9 89 + 11 85 + 15 83 + 17 79 + 21 77 + 23 73 + 27 71 + 29 67 + 33 65 + 35 61 + 39 59 + 41  
;55 + 45 53 + 47 49 + 51 43 + 57 37 + 63 31 + 69 25 + 75 19 + 81 13 + 87 7 + 93 
;*******************************************************************************************************************

(defun is_prime(n)

    (if (= (mod n 2) 0) (return-from is_prime nil))
    
    (setq x (+ (round (sqrt n)) 1))

    (loop for i from 3 to x by 2 do
        (if (= (mod n i) 0) (return-from is_prime nil)(return-from is_prime n))))

           
(defun prime (n)
    (cond ( (= n 2)  nil)
          ( (= n 3) (append (list 3)))
    (t (cond (
       (null (is_prime n)) (prime (- n 1)))
       (t (append (list n) (prime (- n 1)) ))
))))


(defun goldbach (val n)
   (cond ( (null n) nil)
       (t 

            (setq x (car n))
            (setq y (- val x))
            (setq n (remove x (remove y n)))
            (list (format t "~S + ~S " x y))
            (goldbach val n)
      )     
   )
)

(setq value (parse-integer (car *args*)))

(setq prime-list (prime value) )

(print (goldbach value prime-list))