(cgol)$

%  Rabin's probabilistic primality tester.  The value of prime(n) (for LISP
users, say (PRIME N)) will be T or NIL, with a mistake on the average at most
prime_error_rate proportion of uses, assuming the random number generator has
no unfortunate properties.  A composite may be mistaken for a prime, but not
vice versa. %

% commented out by ejs: 2018-10-01 since it appears to not work %
% export prime, witness_count, rab $ %
% The only symbols users of the package may access %

special n, n_1, witness_count, w, sw $

witness_count := 15; w := 2**35; sw:=w-1 $

define brnd(x);    % Auxiliary routine for computing big random numbers%
	if bigp x then random(sw) + w*brnd(x/:w) else random(x) $

define witness();  (brnd(n-2) rem (n-2)) + 2 $

define mexpt(a,j);		% modular exponentiation %
	if j=0 then 1
	else if oddp j then (a*mexpt(a,j-1)) rem n
	else mexpt(a,j/:2)**2 rem n $

define rab(a,j);			% careful exponentiation - %
	if oddp j then mexpt(a,j)	% checks for Carmichaels %
	else let x = rab(a,j/:2);
	     if x<2 then x
	     else if x = n_1 then 1
	     else let y = x**2 rem n; if y=1 then 0 else y $

'rbp' of 'prime' := 10 $

define "PRIME"(n);   % Returns T if n is prime %
  if n<30 then if n isin !'(2 3 5 7 11 13 17 19 23 29) then t else nil
  else 
    gcd(n,6469693230) = 1
  and
     let n_1 = n-1;
     iter for k := 1 step k+1
	for looks_prime := (rab(witness(),n_1) = 1) step ditto
	while looks_prime and k<witness_count 
	return looks_prime $

=EXIT$