Carnival #128 — Primes and Powers!

Here we are at Carnival #128!

In typical fashion, let’s first talk about the number 128, from fascinating number properties to fascinating numerology.

I have to state the obvious — 128 is a power of 2! (and 2!) Specifically \(2^{7} = 128\)

Ok, what else do we know about 128? Well, let’s check the Twitterverse.

@xdoublestar gives this

This led to a nice thread with @jonathanavt

@xdoublestar gives another one to mull over

This leads to more inquiry!

Since we’re on a power of 2 kick. @cardcolm gives this dad joke.

and speaking of jokes, here’s a doozy from @aap03102

But back to 128. Here’s some more numerology.

  • 1283 is the first prime number that contains “128”.
  • Interestingly, 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283 is a 128-digit prime, but notice that if you get rid of the zeros, we have 1283!!! WHAT!!

It gets better, check out these “1283” primes

  • 12 digits: 100000000283
  • 14 digits: 10000000000283
  • 19 digits: 1000000000000000283
  • 28 digits: 1000000000000000000000000283
  • 34 digits: 1000000000000000000000000000000283
  • 124 digits: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283
  • 128 digits: 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283
  • 138 digits: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283
  • 741 digits: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283
  • 752 digits: 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283
  • 754 digits: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283

Finally, consider this. $$2^{168} = 374144419156711147060143317175368453031918731001856$$ what do you notice missing about this power of 2? There’s no 2!! I haven’t been able to find a larger power of 2 that is missing at least one digit.

Ok, enough of this screwball-ery. Where is the content!

Our friend @aap03102 shares this video on doubling and noodle making.

Moving on, @DavidButlerUofA sends in three fun and interesting articles.

The first is about why 65536 is his favorite power of 2.

Next, he’s done some wonderful research on likeable primes! This is a great article with some fun conclusions! Before you read it, take a guess for yourself of what would make one prime number more likeable than another prime number.

Ever hear of the Sausage Stacking Theorem? Well now you have. This is a good lesson about division.

The natural pivot from division is multiplication. Here we have a write-up of a multiplication game from @findthefactors that’s worth checking out.

Leaping incredibly ahead from multiplication / division but still somehow staying in elementary mathland, we have an exploration of Martin Gardner’s hexapawn game from @benjamin_leis.

Next, from @letsplaymath, we have a reminder that about teaching math in a senseful way.

Polite, Funny, And More Types Of Numbers

If there’s anything I like, it’s making up objects, naming them, and studying them. Again from @letsplaymath, we have an activity involving “polite numbers“.

Have you read my take on funny numbers?

Twin, cousin, and sexy primes are discussed in this post sent by @TopCat4647.

Do you know what semi r-primes are?

We have an exploration, authored by @evelynjlamb, of the Edward-Mullin sequence, a curious prime number sequence. There’s also a request to name a special (non-mathematical) temporal occurence … (no spoilers from me!). H/T to @icecolbeveridge for sending the article.

Speaking of primes and how this article started …

Twitter Primes

In all the goofiness around putting together this carnival, I received a lot of fun stuff from the Twitter-sphere as you saw above. But the conversation turned to primes as well.

Check out this thread with what I will call a “Twitter Prime”, that is a prime number that is 280-digits long — 280 characters is the maximum character limit of a tweet.

Finally, today is 27/05/2019, which when written without the forward slashes is 27052019 — a prime!

I hope you enjoyed this Carnival. The next one will be hosted by @mathhombre at his website

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