PHP - Glitchy mod（％）运算符

Question

For some reason: the display looks like this:

3 to the power of x mod 17 is 19. This is called v.

Shared person a (v):
19 

and in the script, it looks like this (this script is used to describe Diffie-Hellman key exchange algorithm.):

$p="17";
$g="3";
$px=gmp_nextprime(rand());
$x=gmp_strval($px);
$a=$g^$x%$p;
echo "$g to the power of x mod $p is $a. This is called v.<br>";
echo "<br>Shared person a (v):<br>";
echo "$a <br>";

Wondering if this is kind of a PHP glitch, because:

if{x mod y=z}, z<y

Now my questions: How to fix this? Had I done anything wrong? Is this a PHP glitch?

(The code needs a clean up, I know.)

Additional notes: $x = 2047401017

Answer 1

Well, ^ is not the power operator and modulo precedes both of them; besides, GMP has a function for power-modulo already:

$p="17";
$g="3";
$px=gmp_nextprime(rand());

$a = gmp_powm($g, $px, $p);

echo "$g to the power of x mod $p is $a. This is called v.<br>";
echo "<br>Shared person a (v):<br>";
echo "$a <br>";