; sieve calls sift, which recursively performs a sieve

(defun sieve2 (n)
   (filternils (sift 2 (ceiling (sqrt n)) (nlist 2 n)))
)

; (sift a b nums) remove all the multiples of numbers from a to b, from nums
; (ie. replaces members of nums with nil)

(defun sift (cnt end nums)
  (cond ((> cnt end) nums)
	(t (cons (car nums) (sift (1+ cnt) end 
						(sift_thru 1 cnt (cdr nums)))
	   )
        )
  )
)

; (siftthru a b nums) strikes off every bth entry in nums (replace with nil)
; a counts from 1 thru the end of the list

(defun sift_thru (i n nums)
   (cond ((null nums) nil)
	 ((zerop (mod i n)) 
	    (cons     nil    (sift_thru (1+ i) n (cdr nums))))
	 (t (cons (car nums) (sift_thru (1+ i) n (cdr nums))))
   )
)

; (nlist a b) recursively creates a list of integers from a to b

(defun nlist (a b)
     (cond ((>= a b) (list b))
	   (t  (cons a (nlist (1+ a) b) ) )
     )
)

; (filternils m) recursively removes all nil's from list m

(defun filternils (l)
   (cond ((null l) nil)
	 ((null (car l)) (filternils (cdr l)))
	 (t (cons (car l) (filternils (cdr l))))
   )
)