Circular Primes

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(C)Copyright 2022, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Maybe I've come full circle. Maybe you saw what others saw a few days ago.

Welcome to Comic #1900. I usually try to make extra effort for the comics ending in 00, but it's been harder for find time to make the effort for regular comics. And for some time, I've been thinking about the year 1900 as a concept for the comic. But, honestly, while things did happen in that year, nothing spectacular popped out at me. Nothing about that year, other than being the last of the 19th century, came to mind.

And then the Calendar problem that I signed up for last month came along. I intended to rework it into a comic, but after four days (six actually, it was submitted before the 13th), I pretty much gave up and decided to use it as is.

The good news is that I can do anything I want for comic 1901. A mini with shapes, a comic with ANTHRO-Numerics(tm), or just teachers or family talking.

And in the back of my mind, I know that Thanksgiving and Christmas are coming, and I really want to enjoy those.

I also write Fiction! You can now order Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Order the softcover or ebook at Amazon. Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Come back often for more funny math and geeky comics.

Prime Time

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

I mean, 8-11 (or 7-10 in your area) doesn't make sense.

Of course, if you just watch video clips, it could be any time. I find I will spend more time watching more short things than one long thing. It's usually because I don't know if I'll sit through (or stay awake for) the long thing. And then a couple hours later, I know that I might have. "Might" -- because there are a number of factors that go into either keeping your attention or knocking you out.

Moira's probably up late. Ken's probably out 20 minutes after the dinner dishes are done. At least for this year.

I also write Fiction! You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Preorder the softcover or ebook at Amazon.

Come back often for more funny math and geeky comics.

Emirp

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(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

It's hard to tell if the emirp is coming or going.

If it isn't obvious, an emirp is a prime number that is still a prime when the digits are reversed. There are also cyclic emirps, where every prime in the cycle is a still a prime when it is reversed.

As for the Weird guy, longtime readers have seen him before.

Come back often for more funny math and geeky comics.

Almost Prime

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(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

They're not ready for Prime Time.

Although you could check Mathflix.

Come back often for more funny math and geeky comics.

New Mersenne Prime

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(C)Copyright 2018, C. Burke.

Joke's on Ken. You can buy a vowel!

First, here's a previous comic from 2008 about Mersenne primes. They've found a few more since then.

For those who don't know, Mersenne primes, they are a special subset of primes that could be written in the form of 2^prime# - 1.

I'd say I'm waiting for the speculation about 2^{Mersenneprime#} - 1, but I wouldn't be surprised if that's already been done.




Come back often for more funny math and geeky comics.

Prime Factorization, Perfect Squares and Irrational Numbers

Moving on from yesterday's discussion about Rational Numbers, what about irrational numbers, numbers which cannot be written as a ratio of two integers?

Most whole numbers have square roots which are irrational numbers, but not everything with a radical is irrational. The square root of a perfect square is perfectly rational. So how can you tell if a number is a perfect square without a calculator?

One way is through prime factorization. (Remember those factor trees from a long time ago. C'mon, they were fun to do -- and you can do them again.... just not when you're typing in a blog. Then, they're kind of a pain, but I'll try.)

Take a number such as 60. It's prime factorization is 2 X 2 X 3 X 5, or 2² X 3 X 5.
If we were to square 60, we'd multiply 60 X 60, but we could also multiply 2² X 3 X 5 X 2² X 3 X 5.
That number (3600) would have a prime factorization of 2⁴ X 3² X 5².

Notice what happened to the exponents. They've all doubled from 1 to 2 or 2 to 4. Every time you square a number, the exponents of its prime factors double. So if a number has been square, then all of the exponents of its prime factors will be even numbers because they are multiples of two.

Going back to our original number, is the square root of 60 a rational number?

It could only be a rational number if 60 were a perfect square, and it can only be a perfect square if all the exponents of its prime factors are even. However, the prime factorization is 2² X 3 X 5. Only one factor is even, so it is not a perfect square and the square root of 60 is irrational.

But wait! There's more!

As long as we've done the legwork, there is one more thing that we can do. Radicals that are irrational can be simplified. This is done by factoring out the largest perfect square. If we look back at the prime factorization, 2² X 3 X 5, we can see that there are two factors of 2.

So the square root of 60 is the same as (the square root of 2²) X (the square root of 3 X 5). The square root of 2² is just 2.
That means that the square root of 60 is (2) times (the square root of 3 X 5), or 2(radical 15).

Cosplay

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(C)Copyright 2014, C. Burke.

Numbers of Cos(play) would be totally rad!.

Hopefully, there are enough buried references to math, sci-fi and this very comic to keep people guessing/wondering/analyzing for a while!

New Largest Prime Found

In honor of the newest largest prime -- and largest Mersenne prime -- ever found, here's a comic from 2008.

The alt-text is out of date now.

Problem of the Day: Factorials

I was going through old papers and torn magazine pages stored in folders that I hadn't looked at in years, finding stuff to recycle. I happened to glanced at a calendar of daily problems, most of which were either too advanced for the classes I was teaching at the time, or just a little too involved. However, one simple problem jumped out at me, and I decided to file that one away for next year. It's definitely a question that needs the solver to explain how he arrived at the answer, and would give me insight into their thinking.

I made a second problem based on the original. Here they both are:

1. Find the largest prime factor of (87!)(88!).

2. Find the largest prime factor of 87! + 88!

Why I love the problems: first, students needed to know something about factors, prime numbers and factorials. Second, seeing a number like 88!, that student whose first instinct is to reach for the calculator will have to put it down and find a new approach.

Answers below. Stop reading here if you didn't figure them out yet.

The answer to problem 1 is fairly straightforward. The factors of 87!*88! are
1 * 2 * 3 * ... * 87 * 1 * 2 * 3 * ... * 87 * 88.
There is no need to make factor trees to find the prime factorization (an approach students might take). The largest prime factor would be the largest prime number not greater than 88. That would be 83.

(If a student guessed 87, show them that 8+7 = 15, which is divisible by 3, so 87 is divisible by 3. Or just have them divide 87 / 3 and see that they'll get 29.)

The answer to problem 2 requires a little work. We want a factor of the sum, but factors are for products, not sums. No problem. Let's make a multiplication problem out of it.

87! + 88!
= 87! + 87!(88)
= 87!(1 + 88)
= 87!(89)

The largest prime factor of 87! is still 83. But 89 is a prime number, so it's the largest prime factor, which is another reason why this is such a neat little problem: 89 isn't in the initial problem, but every whole number less than 89 is!

I think that this is a great journal-type question to assess their understanding of concepts and their ability to communicate a solution. And it will fall in nicely with whatever they're calling "differentiating of instruction" this semester. (Yes, they mentioned a new term at the last department meeting, but I neglected to write it down or even really care.)

P.S. The first problem is mine. The second is the original.

When You Play . . ., Part 2

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(C)Copyright 2011, C. Burke. All rights reserved.


Yes, I know you don't "play" Marines, and it isn't a game,
but I had the image and I was using it!

Sexy Primes

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(C)Copyright 2009, C. Burke. All rights reserved.


Trust me, if you were a walking, talking alphanumeric character, you'd agree.

And then you might want to know what Sexy primes actually are.

47th Mersenne Prime Found

On April 12th, the 47th known Mersenne prime, 242,643,801-1, a 12,837,064 digit number was found by Odd Magnar Strindmo from Melhus, Norway! This prime is the second largest known prime number, a "mere" 141,125 digits smaller than the Mersenne prime found last August.

Mersenne Primes where the subject of a comic from last May:
http://mrburkemath.blogspot.com/2008/05/mersenne.html


http://mersenne.org/

http://science.slashdot.org/story/09/06/13/2218226/47th-Mersenne-Prime-Confirmed

Mersenne

(C)Copyright 2008, C. Burke. All rights reserved.
Be a part of the 45th Mersenne. Ten million digits can't be wrong.



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Or catch it on http://xwhy.comiccgenesis.com.
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Prime Meats

(C)Copyright 2008, C. Burke. All rights reserved.

If they're "prime", would they still call it "product"?

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Or catch it on http://xwhy.comiccgenesis.com.
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11 / 29 / 07 -- Prime Day for Learning Math!

(C)Copyright 2007, C. Burke. All rights reserved.

11, 29, and 7 are all Prime numbers. That's happened a bunch of times this year. However, today is the last time that will happen this year and we have to wait a few years for it to happen again!

2011 is the next prime year (even if you include the "20"!).