Large Clubs
It is an open problem whether there are infinitely large clubs of mutually friendly numbers. The perfect numbers form a club, and it is conjectured that there are infinitely many perfect numbers (at least as many as there are Mersenne primes), but no proof is known. As of June 2009, 47 perfect numbers are known, the largest of which has more than 25 million digits in decimal notation. There are clubs with more known members, in particular those formed by multiply perfect numbers, which are numbers whose abundancy is an integer. As of early 2011, the club of friendly numbers with abundancy equal to 9 has 2091 known members. Although some are known to be quite large, clubs of multiply perfect numbers (excluding the perfect numbers themselves) are conjectured to be finite.
Read more about this topic: Friendly Number
Famous quotes containing the words large and/or clubs:
“Switzerland is a small, steep country, much more up and down than sideways, and is all stuck over with large brown hotels built on the cuckoo clock style of architecture.”
—Ernest Hemingway (1899–1961)
“Neighboring farmers and visitors at White Sulphur drove out occasionally to watch ‘those funny Scotchmen’ with amused superiority; when one member imported clubs from Scotland, they were held for three weeks by customs officials who could not believe that any game could be played with ‘such elongated blackjacks or implements of murder.’”
—For the State of West Virginia, U.S. public relief program (1935-1943)