Project brief (Pb) is a segment of the Gridcoin Fireside where Delta talks about scientific projects apart of the BOINC network in simple terms.

Amicable numbers is a BOINC project run by a small group of people who want to discover as many Amicable numbers as possible.

Now in order to understand Amicable numbers, we must first understand what a perfect number is...

A perfect number is a number where all of its factors (except for the number itself) adds to the number you have.

In the example above, 6 is a perfect number. It has factors:

• 6 (6x1)
• 3 (3x2)
• 2 (2x3)
• 1 (1x6)

So if we take the sum of these numbers except for 6 itself we get:3 + 2 + 1 = 6

Pretty cool right?

So this is where we come to Amicable numbers.

An Amicable number pair is a pair of numbers where each of the factors of each number (except the number itself) adds to the other number.

You can see this in the image above with the smallest Amicable number pair 220 and 284.

As far as research goes, there is no directly applicable problem that uses Amicable numbers however, it does present quite a novelty to crunchers who want to claim those numbers as their own (much like finding prime numbers with Primegrid).