What if no Frederick William I of Prussia

Frederick I, the 1st King of Prussia (Frederick III of Brandenberg) had only 1 surviving son, Frederick William; his 2nd wife, Sophia Charlotte, lived apart from him after a few years and didn't seem to love him as much as he loved her.

So, let's say that Frederick William dies early (he did have porphyria and a violent temper which one could imagine leading to death if not an immediate cause), and the Queen of Prussia isn't interested in trying to have another child. What happens when Frederick I dies in 1713? He has a nephew (also named Frederick William, he of Brandenburg-Schwedt) but his nephew will be a minor for several years yet; would Prussia continue as a kingdom? Given his longer life (if he succeeds in 1713 and lives as OTL, he'd live to 1771)does this alternate Frederick William accomplish things similar to OTL's Frederick the Great? Wikipedia says he was very big on being active but also known for being brutal and short-tempered - so it's also possible he could get involved in wars before Prussia is ready and damage it quite a bit.
 
Well, the fact that Friedrich Wilhelm seemed incapable of producing a male heir until Friedrich der Grosse, was what led his father to remarry to the mad Mecklenburger Venus. So, perhaps if FW dies sooner rather than later, Friedrich I has to remarry post-haste once Figuelotte dies in 1705. If he still remarries but doesn't leave a child, then his nephew would succeed him. However, I do wish to point out, that Friedrich I didn't seem to wish the "royal" title outside of his immediate family, since even after his coronation as king, his half-brothers (the sons of his despised stepmother) were only allowed to style themselves margraves of Schwedt because their mother had bought that territory for her children, but had never stopped scheming that her sons might acede to the electoral dignity. So while he might succeed as Elector of Brandenburg, IDK if Friedrich I will allow him to succeed as king of Prussia, after all, AFAIK, Prussia had passed to Brandenburg through female succession to start with, so maybe the young Wilhelmine (if she's still born, becomes Queen in Prussia, while Friedrich Wilhelm becomes Elector Friedrich Wilhelm II/Friedrich II of Brandenburg. They'll probably marry, who knows, but then she might marry someone else.
 
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