MrHonner

Appreciation Numbers

How Many Primes Did We Miss?

The mathematics world is abuzz with the verification of a new largest known prime number. The number, $2^{57885161} - 1$ , is a Mersenne Prime, and has over 17 million digits. The previous largest known prime was $2^{43112609} - 1$ , which had a mere 12.9 million or so digits.

It’s interesting to note that, while it has been known for thousands of years that there are infinitely many primes, it is a challenge even today to find large ones.

It is also interesting to note how many primes were missed in jumping from the previous largest prime to this new largest prime.

A well-known and elegant result, Bertrand’s Postulate, states that there is always a prime number between n and 2n, for n > 1. For example, the prime 3 is between 2 and 4; the prime 5 is between 3 and 6; the prime 11 is between 10 and 20; and so on.

In particular, this says that there must be a prime between $2^{n}$ and $2^{n+1}$ , since $2 * 2^{n} = 2^{n+1}$ .

Thus, there must be a prime between $2^{43112609}$ and $2^{43112610}$ , and another between $2^{43112610}$ and $2^{43112611}$ , and so on!

Thus, there are at least 57,885,161 – 43,112,609 = 14,772,552 primes between $2^{57885161}$ and $2^{43112609}$ ! We can therefore safely say there are at least 14,772,551 primes between the largest and second-largest known primes!

Let’s hope it’s not another 4 years until we have a new largest prime on the block.

By MrHonner, 12 years11 years ago

Challenge NYT

Math Quiz — NYT Learning Network

Through Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:

Test Yourself Math — February 4th, 2013

This question relates to an article discussing what it means to be “middle class” in New York City. How many months of Manhattan rent equals the average price of a new home in the US?

By MrHonner, 12 years7 years ago

Art Photography

Math Photo: Super Sphere Closeup

A closer look at Bob Stowell’s PolyPuzzle Super Sphere.

By MrHonner, 12 years12 years ago

NYT Resources Teaching

Math Lesson: Teaching the Mathematics of Infinity

My latest contribution to the New York Times Learning Network is the lesson “Teaching the Mathematics of Infinity“.

Inspired by the wonderful article “The Life of Pi, and Other Infinities,” I put together a collection of resources and activities for exploring this rich, mysterious, and important mathematical concept.

Students are challenged to think about the different kinds of infinities encountered in mathematics, and then to research and discuss some of the classic applications and paradoxes of infinity. They are also invited to think about the infinite quantities in their own lives.

Infinity is one of my favorite mathematical concepts: it is an amazingly powerful tool, as well as a rich philosophical idea. The mystery and excitement of infinity always produces great conversations, some of which can go on forever!

By MrHonner, 12 years12 years ago

Challenge NYT

Math Quiz — NYT Learning Network

Through Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:

Test Yourself Math — January 30, 2013

This question has to do with the surge in college and junior college graduates in China. How far behind the US is China in graduations per capita?

By MrHonner, 12 years7 years ago

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