Infinitely Fragile Primes: bonus content!

After I watched the final edit I decided to cut a bunch of stuff and re-do it as a voice-over with me drawing on the maths paper. It was all getting a bit dense and relentless. But by doing more of a recap, some of the content I cut didn't get recreated in the new section. So here it is.

[BaranovPeter]

"...something something pidgeon hole theory."
🤣sounds like every proof I ever wrote.

[MCLegoboy]

Your dog is a scientist. She's trying to find other ways to learn mathematics because simply observing it may not be enough.

[Mattaparker]

Have you ever modelled how many Matt Parker’s there are in the world? I don’t feel remotely unique having such a common name! 😂

[laurendoe]

I noticed the paper was "Dedicated to the fond memory of Ronald Graham" - for whom Graham's Number was named.

[atishayjain]

Hey Matt! Your Content is Amazing. I have been following you from sooo much time. I love your content. It is super informative and cool.

[flymypg]

After a career as an engineer, I'm on the path to becoming a STEM teacher. One of the things I most want students to know is just how "dangerous" a little knowledge can be, how relatively simple tools, used well, can accomplish big things. This mathematical proof is a great instance, even if both the subject and motivation are rather esoteric. The bar is much lower in Computer Science, so that's where I plan to start, using simple tools to launch into some pretty deep theory that is immediately provable.

[sighthoundman]

I once had to return a student's homework that looked like that because my dog did the same thing. They decided not to keep it. (Both the student and the dog.)

[KelseyThornton]

Out of focus Matt made my eyes water trying to see in focus Matt...

[JalebJay]

I loved searching these values when looking for decimal periods of 1/p

[wobblysauce]

So... is your math digestible to a dog?

[witerabid]

Well, at least Sky seems to have great taste.. 🤷

[martijn]

Hmm, aren't the primes that give 1 mod p the primes that factor 10^n-1? Or am I missing something?

[teeweezeven]

Isn't it more simple though?

In this video, you have a prime p and want to find m such that 10^m = 1 mod p.

I may have misunderstood the other video but I thought you have m and want to find p. In that case, it is just searching for the prime factorization of 10^m-1 (or divide by 9 and get something like

Hence 101 is used for 4, since 10000-1 = 3×3×11×101

[lostwizard]

Maybe you don't owe apologies to as many of those students as you think. Did you ever ask any of them to prove they actually have a dog? :)

[TrimutiusToo]

Time for some bonus, patreon peeps style

[krzys]

I think that simpler way to get = 1 mod p is 10^0 = 1 mod p