Super Safi’s Monday Morning Math Mayhem 02 – Perfect Number

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

 

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

So let’s get started this week by continuing our discussion from last week about Mersenne Prime numbers and move on to Perfect numbers.

In the finale of Season 17, Marge and Homer Turn a Couple Play (Season 17, Episode 22), the Springfield Isotopes’s star first baseman Buck “Home Run King” Mitchell is having marital problems with his pop star wife Tabitha Vixx (voiced by This Is Us star Mandy Moore). So when he sees Homer and Marge kissing on the Jumbotron, he asks them for advice. But when Homer is later caught giving a neck massage to Tabitha, both couples break up again – and it is hard for Homer and Marge to give advice when they are not talking to each other themselves.

Towards the end of the episode, Tabitha appears on the Jumbotron asking the stadium crowd to guess the evening’s attendance. At first glance, it appears as though the three numbers are just random numbers. However, as we saw last week, will see today and next week, these three numbers are more than just random numbers.

8,128

The second number on the Jumbotron is 8,128.

8,128 is a perfect number, which is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

8,128 is the 4th Perfect number. The first 4 Perfect numbers are:

6 = 1 + 2 + 3

28 = 1 + 2 + 4 + 7 + 14

496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248

8,128 = 1 + 2+ 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1,016 + 2,032 + 4,064

The first 4 Perfect numbers were discovered by the Ancient Greeks. The mathematician Nicomachus of Gerasa, born in the Roman province of Syria (modern day Jerash, Jordan) had noted 8,128 as early as 100 AD.

The giant of mathematics, Euclid of Alexandria,  proved that 2n−1(2n − 1) is an even perfect number whenever 2n − 1 is prime (to be specific, a Mersenne prime as discussed last week).

For example, the first four perfect numbers are generated by the formula 2n−1(2n − 1), with n a prime number, as follows:

for n = 2:   21(22 − 1) = 2 × 3 = 6
for n = 3:   22(23 − 1) = 4 × 7 = 28
for n = 5:   24(25 − 1) = 16 × 31 = 496
for n = 7:   26(27 − 1) = 64 × 127 = 8128

As you may recall from last week, 3, 7, 31, and 127 are the first four Mersenne primes.

 

Now that we know the secret behind the second number on the Jumbotron, be sure to come back next week when we talk about the third and final number.

Do you remember this episode? Did you catch the number 8,128 on the Jumbotron? Did you recognize the number 8,128 as a perfect number? Are you familiar with Perfect numbers? Sound off in the comments below. You know we love hearing from you.

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10 responses to “Super Safi’s Monday Morning Math Mayhem 02 – Perfect Number

  1. Thank you Safi
    Now I know what my Lucky Number is 😀👍

    Liked by 1 person

  2. Seems most of our mathmatcians are burnt out after spending too many prime hours on last weeks post to appreciate the perfection of this weeks.
    I can’t wait for next Mondays lesson.
    Keep them coming Safi!
    ~MIB👤

    Liked by 2 people

    • Wasn’t there something special about the maximum number of SpringfieldBucks that the game allows too, or did I imagine that?
      ~MIB👤

      Like

  3. Saaaaaaayyyyyy Whaaaaaaaat?
    2+2=? Uhhhh,uhhhhh,pick meeeeee…👋

    Liked by 1 person

  4. This is so cool — I’m not a math person by nature but am finding these posts so interesting! Thanks, Safi!

    Liked by 2 people

  5. Love this!

    Liked by 1 person

  6. Did not remember off the top, but once you point out 1 of those 3 is a perfect number I remembered 8128 is one of them. Well done!

    You must have read that book about the Simpsons’ Mathematical Secrets.

    Liked by 2 people

  7. I would have been upset if you’d talked about perfect numbers without including Euclid’s formula

    Liked by 1 person

  8. Thanks for this great post Safi! IIRC, there is a conjecture which states that all perfect numbers are even 😊

    Liked by 3 people

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