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:
“Private information is practically the source of every large modern fortune.”
—Oscar Wilde (1854–1900)
“We shall exchange our material thinking for something quite different, and we shall all be kin. We shall all be enfranchised, prohibition will prevail, many wrongs will be righted, vampires and grafters and slackers will be relegated to a class by themselves, stiff necks will limber up, hearts of stone will be changed to hearts of flesh, and little by little we shall begin to understand each other.”
—General Federation Of Women’s Clubs (GFWC)