private static function _inc32(string $X): string
    {
        $Y = substr($X, 0, -4);
        // increment counter
        $n = self::strToGMP(substr($X, -4)) + 1;
        // wrap by using only the 32 rightmost bits
        $Y .= substr(self::gmpToStr($n, 4), -4);
        return $Y;
    }