Mersenne Primes and Perfect Numbers: A Love Story by Dan Garbowitz

GRCC Adjunct Mathematics Instructor Dan Garbowitz talks on how prime numbers and perfect numbers have fascinated professional and amateur mathematicians for centuries, and much about them remains unknown. This talk will provides glimpse of the beauty and mysterious nature of these numbers and the relationships between them. Perfect numbers were known to the Greeks and have been studied since at least the 3rd century B.C. Marin Mersenne, a 17th century theologian and mathematician, developed a list of prime numbers, all with the same interesting form. Sometime later, Leonard Euler proved a fascinating statement that related the perfect numbers to the Mersenne Primes. During this seminar we will investigate this theorem in particular, and other number theory topics relating perfect numbers and Mersenne Primes.

[dataandcolours]

Good lecture and solid methodology for the proof the other way around.

Just a note for anyone watching this from now on: It's important to emphasize that the sigma function is only multiplicative if the factors involved are relatively prime (no common primes between them). Yes for all your examples here they are relatively prime and there is nothing wrong with any of the logic presented.

But for people seeing this video that are relatively new to number theory, they may easily misunderstand it to being more general than it is. For instance since 6 and 21 is not relatively prime since they have a 3 in common. However you could find sigma(126) by doing Notice in contrast that sigma(6)*sigma(21) is 12*28=336.

[mercedesmalone]

thank you so much for this! I love it so much!

[selenawallace]

Great video, I learned more watching you this than I did in my class