Off the Number Line: Odd Perfect Number

funny math cartoon


There’s a unicorn standing there but these two explorers are only interested in the number. Too funny…


What? There’s a unicorn? Oh, yeah.


Okay, so tell me. What exactly is an “odd perfect number?”


A “perfect” number is a positive integer that is equal to the sum of all of its proper divisors. The first perfect number is 6 because the divisors of 6 are 1,2 and 3, and 6 equals 1+2+3. The next is 28, because 28 = 1+2+4+7+14. It turns out that perfect numbers are very rare and they all seem to be even.


So, it’s not possible for a perfect number to be odd?


Mathematicians haven’t ruled out the possibility yet. There’s a group at oddperfect.org that has an ongoing computing project to try to find one, but it’s already into the hundreds of digits and becoming increasingly unlikely that odd perfect numbers exists.


The open possibility that an odd perfect number could exist makes them even more fascinating than unicorns, which we know are fictional. Very cool. Looking forward to what I’ll learn from next week’s Off the Number Line cartoon!


Further reading:

Matthew Peterson and James Huang

About the Author

Matthew Peterson, Ph.D., is Co-founder and Chief Research & Development Officer at the MIND Research Institute. James Huang is Senior Visual Designer at MIND Research Institute.


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