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:
“He began therefore to invest the fortress of my heart by a circumvallation of distant bows and respectful looks; he then entrenched his forces in the deep caution of never uttering an unguarded word or syllable. His designs being yet covered, he played off from several quarters a large battery of compliments. But here he found a repulse from the enemy by an absolute rejection of such fulsome praise, and this forced him back again close into his former trenches.”
—Sarah Fielding (17101768)
“Women realize that we are living in an ungoverned world. At heart we are all pacifists. We should love to talk it over with the war-makers, but they would not understand. Words are so inadequate, and we realize that the hatred must kill itself; so we give our men gladly, unselfishly, proudly, patriotically, since the world chooses to settle its disputes in the old barbarous way.”
—General Federation Of Womens Clubs (GFWC)