In what amounts to a matter of Why Is This Important? (to which the answer is, It Isn't) I happened upon Amicable Numbers (see Wikipedia on this) and apparently this was some project that the great mathematician Leonhard Euler devoted some time to. Euler discovered 59 pairs, adding to the three that were then known to exist. But there are now apparently 11,446,960 known amicable pairs, and the largest of these has 24,703 digits! See the website devoted to giving all of them: http://amicable.homepage.dk/knwnc2.htm.
While fascinating to a certain extent, one has to wonder what use amicable pairs are. A paper I found on the net, at http://ftp.cwi.nl/CWIreports/MAS/MAS-R0307.pdf discusses amicable pairs in depth, but never says anything about any possible practical use of research on the subject. Mathematics at its purest, I suppose.
Just as an interesting exercise, I built a program to discover, by brute force, all amicable number pairs smaller than 20,000. I let the program run to completion and at the end it had found the following pairs:
Which check out nicely on the AP website.
Remember Me