(defun erath (n)

  (let ((a (make-array n))
        (res nil))
        
    (loop with i = 2

          while (< i n) do

          (if (null (aref a i))

              (let () 
                (setf res (cons i res))
                (loop for j from i to (1- n) by i do
                      (setf (aref a j) t))))

          (setf i (1+ i)))
    (reverse res)))


(defun mupol (l k)
  (loop for x in l sum (expt x k)))

(defun prime-list (k acc nrem pl)

  (cond ((= 0 nrem) 
         (if (check-ok k acc)
             (progn
               (format t "~S ~%" acc)
               (throw 'list-found acc))))
        (t (loop with pl-akt = pl while (not (null pl-akt)) do

                 (prime-list k (cons (car pl-akt) acc) (1- nrem) (cdr pl-akt))
                 (setf pl-akt (cdr pl-akt))))))

(defun check-ok (k acc)

  (let ((res (loop with res = nil for l from 1 to k do (setf res (adjoin (mupol acc l) res)) finally return res)))
    (format t "~S ~%" res)
    (= k (length res))))

                 
(defun get-primes (k)

  (catch 'list-found (prime-list k nil k (erath 100))))