Super Safi’s Monday Morning Math Mayhem 05 – Chen Prime, Sophie Germain Prime, Newman-Shank-Williams Prime

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?

This week, we continue our journey by looking at none other than Homer Jay Simpson’s weight.

In a few episodes, we’ve seen that Homer Simpsons weighs 239 pounds, despite the fact his drivers licence indicates 140 pounds.

The first occurrence is in Season 1, Episode 10, “Homer’s Night Out”. Homer weighs himself and resolves to exercise. Six months later he weighs himself again and again resolves to exercise. Both times he weighed exactly 239 pounds.

“Homer’s Night Out” opening sequence

“Homer’s Night Out” six months later

The next, arguably more memorable, look at Homer’s weight is in Season 7, Episode 7, “King Size Homer”. In the episode, Homer despises the nuclear plant’s new exercise program, and decides to gain 61 pounds in order to claim a disability and work at home. Here too we see Homer weighs 239 pounds.

Homer’s road to success in “King Size Homer”

Homer qualifying for disability in “King Size Homer”

239

239 is a prime number. However, as you may recall from four weeks ago when we discussed Mersenne Primes or last week when we discussed Fermat Primes, primes can often be sub-categorized based on common properties. While not a Mersenne Prime or Fermat Prime, 239 can fall into a few categories of primes.

First, 239 can be considered a Chen Prime. A prime number n is called a Chen Prime if n + 2 is either a prime or a product of two primes (also called a semiprime). Chen Primes are named after Chinese mathematician Chen Jingrun (pictured below) who in 1966 proved an infinite number of such primes exist.

239 is considered a Chen Prime as 239 + 2 = 241, and 241 is also a prime number. While together, 239 and 241 are known as Twin Primes, it is 239 as the lowest of the Twin Primes that gets the designation of Chen Prime.

Secondly, 239 can be considered a Sophie Germain Prime. A prime number n is called a Sophie Germain Prime if 2n + 1 is also a prime. The resulting 2n + 1 prime is called a Safe Prime. Sophie Germain Primes are named after French mathematician Marie-Sophie Germain (pictured below) who who used them in her investigations of Fermat’s Last Theorem.

239 is considered a Sophie Germain Prime as 2 x 239 + 1 = 479, and 479 is also a prime number, more specifically a Safe Prime. 239 is the 17th Sophie Germain Prime; following 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, and 233.

Thirdly, 239 can be considered a Newman-Shank-Williams Prime. A prime number is called a Newman-Shank-Williams Prime if [(1 + √2)^^{2n + 1} + (1 – √2)^^{2n + 1}] / 2 is prime. 239 is the third Newman-Shank-Williams Prime and is generated by plugging 3 in for n in the aforementioned equation. The first two Newman-Shank-Williams Primes are 7 (plugging in n of 1) and 41 (plugging in n of 2). Newman-Shank-Williams Primes were first described by American mathematicians Morris Newman, Daniel Shanks and Canadian mathematician Hugh C. Williams in 1981.

Aside from being Chen Prime, Sophie Germain Prime, and Newman-Shank-Williams Prime, 239 also has significance in chemistry. 239 is the atomic mass number of the most common isotope of plutonium, Pu-239.

Plutonium-239 is the primary fissile isotope used for the production of nuclear weapons, although uranium-235 has also been used. Plutonium-239 is also one of the three main isotopes demonstrated usable as fuel in thermal spectrum nuclear reactors, along with uranium-235 and uranium-233.

Now we know the significance of Homer’s weight. Knowing how mathematically and scientifically inclined the writers of The Simpsons are, we can safely assume that it is no coincidence that Homer’s weight was selected as 239.

Did you know the significance of the number 239? Are you familiar with Chen Primes? Are you familiar with Sophie Germain Primes? Are you familiar with Newman-Shank-Williams Primes? Sound off in the comments below. You know we love hearing from you.