%!
% A PostScript file must start with the two characters "%!",
% else the printer will print it literally instead of interpreting
% it as PostScript.  Since any line beginning with % is a comment
% in this language, the first %! line is not itself run as PostScript.

/erath{
% define a procedure erath, which when invoked with "x erath" for
% some integer x returns a boolean array siv of length x+1 (since
% PostScript arrays are indexed from zero) whose n-th element is
% "true" if n is prime, "false" otherwise.

  /x exch def
% store the argument in the variable x

  /siv x 1 add array def
  2 1 x { siv exch true put } for
  0 1 1 { siv exch false put } for
% initialize siv so its 0th and 1st elements are "false", the rest "true"

  2 1 x sqrt{ /p exch def siv p get {
% loop over primes from 2 to sqrt(x)

  p p add p x {siv exch false put} for
% set the 2p-th, 3p-th,... elements of siv to false

  }if }for siv} def
% wrap up and push siv on the stack

% sample application: print all the primes up to 2000

% first select a font and define a `carriage-return' utility "cr"
% and a right-justification routine `rightjustify'
/Times-Roman findfont 10 scalefont setfont
/leftmargin 100 def
/pagetop 680 def
/pagebottom 80 def
/columnwidth 60 def
/spacing 13 def
/cr1{ leftmargin currentpoint spacing sub exch pop moveto }def
/cr{
  cr1 currentpoint pagebottom le 
  {/leftmargin leftmargin columnwidth add def leftmargin pagetop moveto}
  if pop
  } def
/rightjustify {dup stringwidth pop neg 0 rmoveto show} def

% run the Sieve on x=2000 and pop siv off the stack
2000 erath pop

% move to top of 8.5"x11" page and print heading
230 720 moveto
(PRIMES UP TO 2000) show leftmargin pagetop moveto

% create a character string "str" to hold the 4-digit primes
/str (    ) def

% and show them ("cvs" = convert to string)
2 1 2000 { dup siv exch get {str cvs rightjustify cr} {pop} ifelse} for

% finally print out the page
showpage