What are the two rumors at the beginning of Chapter Four about Gatsby?

The rumors about Gatsby at the beginning of Chapter IV of The Great Gatsby (Fitzgerald) are quite different in nature.  The first is that Gatsby is a bootlegger.  To put this in some context, selling or producing alcoholic beverages was illegal during this period in the United States, an era we call "Prohibition." This in no way stopped people from drinking, and bootleggers were there to help them do so, smuggling in alcohol from other countries, such as Canada. The notion of Gatsby as bootlegger was consistent with the times, his stunning wealth, and his associations with organized crime.  The other rumor was that Gatsby had killed a man once, a man who had discovered Gatsby was Paul von Hindenburg's nephew.  Von Hindenburg was an officer in Germany in World War I and a rising politician who would become president of Germany. The prejudice against Germany was quite strong during the period in which the novel takes place because the United States and Germany had been enemies in World War I. Indeed, even Americans citizens of German descent were often treated with suspicion during this period.  So, if Gatsby had been a nephew of a prominent German politician, the idea was that he would have killed a man to keep this from being revealed.  Gatsby is not concerned with all the rumors that swirl about him. They make him more interesting, they might attract Daisy's attention, and they help him to conceal his mundane origins.