In 1453 the Sultan of the Ottoman Empire, Mehmed II conquered Constantinople and absorbed the last of the Byzantine Empire. Mehmed was 21.
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The last Emperor of Constantinople was Constantine XI, the final Caesar to rule Rome, but that was not their supposed end, it is however alleged that the Emperor's niece married into the rulers of Russia, and so the word Tsar, or Caesar was taken as title of ruler ship for the leaders of that nation, who considered themselves the Third Rome. This line was put to an end by the Bolshevik Revolution, when Nicholas II and the royal family were killed.
One might think that Rome, being the sexually liberated place that is was would have produced a lot of Caesars, genetically if not legally, Julius was called the Bald Adulterer in addition to his title of Unconquerable God. But truth be told there were not that many illegitimate births in Ancient Rome because the Romans had an Herbal remedy that served as a morning after pill, Silphium, which was used to the point that only the memory of it lives on, the plant had been driven to extinction.
Even if this was only in vogue for a century or two there were other barriers to the passing of the divine lineage of Caesar, that many of them were gay or bi-sexual, driving down the number of possible accidents that might result in unwanted child support payments. Julius Caesar for instance is known for the famous line in Shakespeare's play, "Et tu, Brute?" Naming one of his numerous assassins, Marcus Brutus. This line was often explained that they were friends, which is likely; alternatively that they were illegitimate Father and son, which is unlikely as Julius was only 14 or 15 when Brutus was born; and what I think is the most likely explanation, they were gay lovers, as it was said that Caesar covered his face and surrendered to the assassins when he saw that Brutus was in their number, and that level of betrayal makes sense.