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Sylvester: Ushering In The Modern Era Of Research On Odd Perfect Numbers, Steven Gimbel, John Jaroma
Sylvester: Ushering In The Modern Era Of Research On Odd Perfect Numbers, Steven Gimbel, John Jaroma
Philosophy Faculty Publications
In 1888, James Joseph Sylvester (1814-1897) published a series of papers that he hoped would pave the way for a general proof of the nonexistence of an odd perfect number (OPN). Seemingly unaware that more than fifty years earlier Benjamin Peirce had proved that an odd perfect number must have at least four distinct prime divisors, Sylvester began his fundamental assault on the problem by establishing the same result. Later that same year, he strengthened his conclusion to five. These findings would help to mark the beginning of the modern era of research on odd perfect numbers. Sylvester's bound stood …