<p id="prvi">
            bla bla bla kurac tekst bla bla bla
</p>


            <input type="button" value="Bojanje" onclick="setColor();"/>

                <script>
                    function setColor(){
                        bgColorCode = '#'+Math.floor((Math.Random() * 999999)+ 100000);
                        elements = document.getElementByClassName('prvi');

                        for (var i = 0; i < elements.length; i++) {
                            document.getElementByClassName('prvi')[i].style.backgroundColor = bgColorCode;
                        }
                    }
                </script>