--  primes.min: compute primes using Sieve of Eratosthenes
--  (http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
--
--  Compute primes up to a specified n by crossing out multiples of successively
--  larger primes in a boolean array.  The array stores a[k] = 1 if k is composite
--  (not prime), and a[k] = 0 if k is not divisible by the divisors considered
--  thus far.
-- 
--  Requires a specified integer n as input, assumed to be < 1000.

program primes;

n : integer;
a : array(1000) of integer;	-- prime candidates array
i, j : integer;
x, sqrt_n : integer;

beginprogram	-- main program
    -- compute the square root of n and put the result in sqrt_n
    read n;
    x := n;
    while x > n / x loop
	    x := (x+n / x) / 2;
    endloop;
    sqrt_n := x;

    -- initialization of the array
    i := 2;
    while i <= n loop
	    a(i) := 0;
	    i := i + 1;
    endloop;

    -- make the array
    i := 2;
    while i <= sqrt_n loop
	    if a(i) = 0 then
          -- i prime, so eliminate its multiples
	       j := i+i;
	       while j <= n loop
		       a(j) := 1;
		       j := j+i;
	       endloop;
       endif;
       i := i + 1;
    endloop;

    -- print primes
    i := 2;
    while i <= n loop
	    if a(i) = 0 then
	       write i;
       endif;
       i := i + 1;
   endloop;
endprogram