A primogen claiming another title and contesting, is still a primogen?

Given a scenario such as this one:
Player 1 has Vampire A who is a primogen.
Player 2 has a Vampire B who is a prince of London.

Vampire A attempts to seize the title of prince of London.

Vampire A and Vampire B, therefore, start contesting the prince of London.

A couple of rules related to this question:

"If more than one vampire claims the same title, then the title is contested".
"the vampires involved in the contest are treated as if they have no title, but they remain controlled and may act and block as normal"
"A vampire cannot have more than one title"

The question therefore is: does Vampire A, while the contesting is taking place, keep the primogen title?

No, vampire A lost the Primogen title when they gained the title Prince of London which was then immediately made dormant because of the contestation.