That was probably the driving force for leaving all over Europe and the British Isles starting as soon as Europeans and Brits started flocking over in the 16th-17th century-the laws of primogeniture only gave the oldest kid an inheritance-so it made sense for the rest of the kids to get passage to the new world-as a soldier, sailor, domestic servant or whatever other way they could get there-much easier to get established in a new place-with a new identity, too if you had the King’s attention by being a rebel from Spain, Scotland, Ireland, France, etc-nobody here cared why you were here as long as you worked and didn’t do bad things to your neighbors...
Yes, the primogeniture was a big thing in many countries. In Scandinavia, on the other hand, they divided the land among all the sons, until nobody had enough land to grow a turnip stew.
The United States is still awfully empty, as my daughter found when she drove from Seattle, WA, to Wilmington, NC.