937? That's positively modern, surely you're don't doubt our shared pedigrees to your 46th/my 48th great-grandfather Gjúki in the 4th century? Then there's Cormac Gealtach, whose legendary pedigree butts right up against the life of Christ and probably isn't "quite" in line with WikiTree policies and standards.
Seriously though, as much as I doubt most of the 100,000+ paths of descent each of us has to figures like Gjúki, I'm just as sure we do both descend from him. It's a mathematical near-certainty (to the extent that Gjúki is a historical figure at all). That would certainly hold for figures like Charlemagne (for Northwest Europeans generally), William the Conquerer (anyone deeply British), Robert the Bruce (Scottish ancestry), and Edward Longshanks (English ancestry). And for those at least I have some lines with a higher degree of confidence.