prime.el

(define (check-prime? n d)
	(cond
		((and (not (= n d))(= (remainder n d) 0))(display "it's not a prime\n"))
		((= n d) (display "it is a prime\n"))
		(else (check-prime? n (+ d 1)))))

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

(define (find-divisor n test-divisor)
	(cond ((> (square test-divisor) n) n)
	      ((divides? test-divisor n) test-divisor)
	      (else (find-divisor n (+ 1 test-divisor)))))
	
(define (divides? a b)
	(= (remainder b a) 0))

(define (square n) (* n n))

;(define (prime n)
;	(check-prime? n 2))

(define (prime n)
	(= n (smallest-divisor n)))
 

(define (next-prime n)
	(if (prime n) 
		n
		(next-prime (+ n 1))))

(define (lpd n p lp)
	(let ((next (next-prime (+ 1 p))))
	(cond ((= (remainder n p) 0) (lpd n next p))
	      ((> (/ n 2) p) (lpd n next lp))
	      (else lp))))

(define fast-prime n)
	(find-next-divisor
			
(define (larget-prime n)
	(lpd n 2 1))

;(if (prime 7)
;	(display "it's a prime\n")
;	(display "it's not a prime\n"))