Primogeniture was pretty common in the middle ages in Europe. I've read arguments that it's a big reason why the Normans basically went out conquering England, the Mediterranean, etc.
Primogeniture doesn't really set in until the High Middle Ages, and even then, there was still a fair amount of splitting inheritance up among sons (that's why the Holy Roman Empire consisted of so many small states: some of the duchies were given to splitting up to give to second and third sons).
The Norse themselves still tended to follow partitioning laws, at least until the Scandinavian kingdoms started to coalesce. The repeated invasions of England between Ethelred the Unready and the final conquest of William the Bastard were not driven by second sons needing kingdoms for themselves, it was driven by England having the best tax base in the North Sea but high political stability, as well as the dying out of family lines.
Key point about the latter: when Edward the Confessor died without issue, the claims to the English throne were:
* Edward's brother-in-law and most powerful vassal, Harold Godwinson (son of the person who put Edward on the throne in the first place)
* William, the bastard son of Edward's maternal cousin. Bolstered by "when he was staying over when he was young, he totally promised me the throne when he died."
* Harald Hardrada, whose claim is "Cnut was King of England. He died, so his claim passed to Harthacnut. Harthacnut and Magnus made an agreement that, should one die without issue, the other would inherit his lands. Harthacnut died without issue, so Magnus should have been King of England. Magnus died without issue, so his claim winds its way back to me, his father's half-brother by way of mother."
