I learn from CGPgrey video that the Royal family is the direct descendant from William the Conqueror which would make it a recorded line stretch back a thousand year which is pretty impressive for most of us who know our allegedly direct ancestors at best 3 or 4 generations back. I say allegedly because with modern DNA technology people starts to find out left and right that they are not descent from whom they are supposed to be even as few as two generation back (grand parents). I realize a cheating female descendant from William won't broken the line, the line can only be broken is by a cheating consort. So what are the chance that they are related and if not at which point that the recorded line was broken by a cheater?
Check out /u/dmahr's answer to a related question: how did royals know if their children were really their children
As his answer shows, the surprise discovery of Richard III's body yielded DNA tests with a that provided strong genetic evidence of this scenario (and these findings "broke out" to general news outlets).
I think you've also potentially asked a slightly different question then you realized as there are many scenarios where "secret royal bastards" were sired by another noble figure who can trace his roots back to Billy the Conq. I'd love to see if anyone has tried to deal with this tougher problem.