How to Easily Identify Any 2-Digit Prime Number

[@ComboClass]

(I noticed a little problem with the version of this I uploaded a few hours ago, so I took that down and here’s the fixed version. Hope you all enjoy!)

[@Somebodyherefornow]

what was broken

[@ComboClass]

@@Somebodyherefornow I realized that near then end when I mentioned how to extend the technique to larger number ranges, I left out some necessary details, so I fixed that scene and title card to be more accurate/clear. The first 13 or 14 minutes of the video are the same as that previous version

[@StoicAtol21445]

When you do your video on counting in different bases, you should colab with Jan Misali!!

[@ComboClass]

@@StoicAtol21445 I would be down. I've only seen a few of their videos, but they are cool and unique. I don't know if they do any collabs, but I recently noticed they left a comment on one of my older videos!

[@StoicAtol21445]

@@ComboClass I know that they did a colab once before about counting in different bases, that's actually what gave me the idea.

[@GirishManjunathMusic]

Just before he mentioned 49 it clicked that he's basically walking us through the concept of Eratosthenes' Sieve which I hadn't understood intuitively yet until this video anyway. Very nice video!

[@zoeyhewll9199]

yes! he's approached the sieve from an angle I hadn't seen it from before, which removes a lot of apparently redundant checks

[@Gin-toki]

Just discovered your corner of the internet and I really dig it! You are good at explaining the subjects and you cover some rather interesting ones. And the chaos is just brilliant xD

[@Omlet221]

I had a no calculator test today and one of the answers contained the root of 119 so I almost left it not simplified because I couldn’t think of any factors. It eventually struck me that 119 is 70 plus 49 so I got it thankfully. I wish I would’ve watched this video a long time ago! I had no idea of the multiple of three test and multiple of seven test, that’s so useful!

[@rhandhom1]

That's not how factors work.

[@Dirt.]

@@rhandhom1 i think they meant that they realized 7 was a factor, since it was the sum of two multiples of 7. Hope this helps :)

[@Omlet221]

@@rhandhom1 Oh wait your right, I don’t remember what I did then then. Maybe that was my proof that I didn’t have to simplify it? It’s hard to remember a test you took afterward because it’s so much thinking lol 😅 I will update when I get that test back what the problem actually was. I think it was maybe sqrt(117) which simplifies to 3*sqrt(13). Still this video was pretty useful because I would’ve noticed the threeven test.

[@torydavis10]

I had a calculus teacher in high school who liked for us to notice that sqrt(ab)=sqrt(a)sqrt(b). Might've been a weird quirk of his, but I feel like it was good training for the mental gymnastics of u substitutions and dividing out weird expressions to make everything look like the derivative of something reasonable.

[@Mathias.skew.7]

​@@Omlet221so?

[@jonathangruber7793]

Recently found your channel. As a mathematics enthusiast I have been thoroughly enjoying your content. Please keep up the stellar work, sir! P.S. Love the little "mishaps" that occur in your videos. Makes me chuckle every time. Lol!

[@arostheautistic1045]

>how to easily identify any 2-digit prime number >15 minutes 27 seconds I'm just joking man, great video again. One of my favorite things has always been the threeven and multiple-of-9 tests. The proof using modular arithmetic is really satisfying.

[@publiconions6313]

Im hooked sir -- one of the few channels i drop everything else to watch as soon as i get the notification : )

[@iamwhatitoture]

I love that your videos truly capture the mind of a matematician. It's beautiful.

[@cookiequeen5430]

This is what got me hooked back in 2020 to start memorizing primes. It's surprisingly easy!

[@twixerclawford]

I actually applied this "square root of prime" checking test in some code I wrote in high school to significant speed up the program! It's an extremely handy trick, one that seems too good to be true, but it is!

[@itsiwhatitsi]

Hi Combo Class I am here to say hello and how are you? I like your originality in general 👍 I think it’s a lost value nowadays and sometimes not always considered in the right way. Keep it up with the good work

[@faeancestor]

this entire setup makes me really anxious

[@HipsterShiningArmor]

one neat thing about 91 is that it is a triangular number, and no triangular numbers (aside from 3) can be prime, so while i do probably agree that its the hardest 2-digit prime to spot, its not that difficult if you know how to find it 119 is truly treacherous though

[@publiconions6313]

Would be cool to see some deep dives on Pascals tri.. the 1s.. the naturals.. the triangular numbers.. skip a few.. the cubes.. why the skips?.. where do the primes fit in.. I'm sure I'm 500 years behind, but something about the way he does it really makes me "ken" the thing

[@josephrissler9847]

No matter how many times I look at 7x17, my brain just won’t accept 119 is composite.

[@johanneschristopherstahle3395]

It becomes so much easier as soon as you realize that numbers ending on 1 must have factors that either both end on 1 or one ending on 7,the other on 3. 3 is either 1 and 3 or 7 and 9 7: 1 and 7 or 3 and 9 9: 1 and 9 or 3 and 3.

[@maxanimator9547]

Prime squares make so much sense I'm ashamed I did not think of this exclusion method by myself.

[@fish-o]

Your vids are amazing man! You genuinely make me excited to learn more about math 😃

[@tenhletypektady]

just discovered this channel and i love it

[@alexdamman6805]

Thank you so much for saying One Hundred Twenty-One when many people say One Hundred and Twenty-One. You could compare it to an unjustifiable grammar rule however it is more understandable. Anything we can do like this truly helps.

[@stevesmith2044]

In England it sounds odd missing the and. It must be a cultural thing.

[@BooBaddyBig]

I was always a bit nervous about numbers like 71 or 83, is that prime or not and would have to try dividing it by 7, but of course you don't have to because it's not 49 nor divisible by 2,3,5. NICE TRICK!!

[@Mr.D.C.]

Domotro is the embodiment of chaotic good

[@bobh6728]

I’m imagining that his house is immaculate with everything in its place.

[@ChongFrisbee]

It is not easy to explain why this works in a short video like this, but you can apply mod to sections of numbers and retain the remainder. So, for the examples from 7*7 to 11*11, you can do something like 91 -> (9%7)1 -> 21 -> 0 119 -> (11%7)9 -> 049 -> 0 97 -> (9%7)(7%7) -> 20 -> (-1) -> 6 note the 0 in the 119 example is important for larger examples or if we wanted to do it differently 119 -> 1(19%7) -> 105 -> (10%7)5 -> 35-> 0

[@ChongFrisbee]

Well, I said it's not easy, but it probably isn't that difficult either, come to think of it. In essence this operation is just subtracting some multiple of 7, with some abstraction added to make the operation simpler/faster to execute

[@ChongFrisbee]

By the way, one of the most eye opening things for me was realizing that division is iterated subtraction (as the log is iterated division). I mean, it had to be since division is the inverse of multiplication, which is iterated sumation (whose inverse is subtraction). But still, I wish this point was made more poignently (if that is a word) in school

[@larswilms8275]

I always call this the remainder long division. You do not care about the answer of the long division just that you are left with 0 as the remainder at the end.

[@ChongFrisbee]

@@larswilms8275 Nice way of thinking about it! The name would suggest doing it left to right, but I guess nothing is perfect. I'll use this name from now on. Don't imagine I'll come up with something better anytime soon

[@larswilms8275]

@@ChongFrisbee Well If you want right to left: Since 1001 is divisible by 7 a similar trick to the 11 divisibility can be created. Take a number and divy it up in groups of three starting from the right 12345678912 => 12|345|678|912 now from right to left alternate added and subtracting the groups. 12|345|678|912 => 912-678+345-12 = 1257 - 690 = 567 If this number is divisible by 7 the original number is divisible by 7. 567 = 560 + 7 = 80 * 7 + 1 * 7 = 81*7 or do the three digit trick for 7 567 ==> 56 - 2 * 7 = 42. 42 is divisible by 7 so the number is divisible by 7 12345678912 = 1763668416 * 7

[@CheeseAlarm]

As a child I learned my times table up to 12. So a naive 2 digit primarily test is "is it in the times table?" This fails on 51 and 91 the Sneaky Composites. There's 69, 93 too but they don't even try to hide their threevenness.

[@ra1nman_mashups]

13:26 one of my old professors said 91 was a prime and the whole class looked at him like 😮

[@unexpected2475]

Here's a very odd comparison: you remind me a lot of the youtuber Explosions&Fire, just in some of your chaotic presentations (also you look very vaguely similar). You guys are both pretty cool, so it is a compliment. Don't know if anyone else thinks this. (also for some reason auto-captions think your name is "jumotrell"?)

[@yogiberraslovechild3080]

So if you implement the sieve of Eratosthenes in a computer program, you only have to check the primes up to the square root + 1 of the number you are testing, not all the primes you've found!

[@ComboClass]

You wouldn't even need to do +1. You can just check all primes up to the square root (and including the square root if it's a whole number and prime). Then there would be further shortcuts about how you would only need to multiply those primes with combinations of other primes

[@MRTACPANS]

We Can Even Seperate By Syllables and Addem up together . 11*2 13*4 17*8 23*5 and so forth 52 Composite *7 63 composite is 9. but we can acheive this by another Method. Note What the CUbes Can do

[@user-cj9fk8un3i]

i enjoyed it a lot!

[@samuraisecretary]

Maybe easier 7 test: Zeroth, this is all mod 7, after every step below, if it's easy enough to mod 7, go ahead. •First, take the 10s place digit (mod 7). •Second, triple it (mod 7). •Third, take the 1s digit (mod 7). •Fourth, add results two and three (mod 7). •Last, did you get 0? (Or 7 depending on how you think about modular arithmetic?) That number's divisible by 7. Bonus note: This expands to numbers of any length. Add digit, triple, add next digit, triple, repeat, repeat, add digit, is it 0? Example: 84 8 mod 7 is 1 Times 3 is 3 Plus 4 is 7 Yup, divisible by 7. Why?: Because 10 mod 7 is 3 and you're just reading the number. 84 is 8 times 10 plus 4, which is the same as 1 times 3 plus 4 in mod 7.

[@jyrinx]

This is about to be a great link for sending to confused Magic players

[@skinisdelicious3365]

I love the schizophrenic energy of your videos

[@Somebodyherefornow]

nth where n is a unknown variable)

[@jensknudsen4222]

No need to add fire. Your videos already made me nervous.

[@Justyouraveragedaeodon5]

Can you do 3 digit numbers next ?

[@ComboClass]

The 100s wouldn't be too hard, but by the time you got to about the 300s, there's not going to be a very easy technique to know them all from memory without memorizing a bunch of things. However, there's a chance I could return to this topic with a further range someday

[@Justyouraveragedaeodon5]

@@ComboClass thanks

[@glorydragon2597]

okay so basically, to tell if a number is prime: 1) Determine if it is composite or not 2) There's your answer

[@Argue625]

Did you kill the wasps and then intentionally pull off the paper cover to show the hexagonal larval chambers? Nice touch.

[@ComboClass]

What are you talking about? There's no wasps in this video. If you are talking about the wasp nest in a previous video, somebody mailed that to me

[@Kastor774]

When did Explosions & Fire change careers?

[@robharwood3538]

Couldn't you extend 'threeven' as 'a multiple of three' into 'a multiple of five' as 'fiven'? Doesn't work for seven, unless you go 'sevenen', but other than that, fiven could be useful.

[@PhngluiMglwnafh]

Burnt dice fumes -- don't breathe this!

[@ComboClass]

Yeah I try to avoid burning plastic. A few dice may have snuck into this one though

[@AntonioFerreira-mx1er]

Your content is very good, those distractions with fires and things collapsing is exagerated and actually reduce the quality of the videos.

[@plushloler]

Please keep yourself safe!

[@robertweekes5783]

The main trick at 13:40 ⏰

[@user-ox4ii2bw6x]

Lethargic trick, try 6x±1 instead and working out that the spit out factor is prime.

[@avaevathornton9851]

120 is the smallest positive integer multiple of 6 that isn't adjacent to a prime number.

[@emilyrln]

Seems like every video Domotro passes through fire and water… Domotro is Gandalf? 😂

[@papergoat9]

I remember sm saying 6N+\-1 but it isn’t true I. Some cases like perfect squares

[@MuffinsAPlenty]

It's true that every prime number larger than 3 must be of the form 6n±1. I don't know if that's what you're thinking of or not.

[@papergoat9]

@@MuffinsAPlenty that is

[@joefarrow1599]

Yeah really cool, so it's basically, "take out 91 and you're good the rest are obvious enough", that's nice

[@monoman4083]

this will get mega views..

[@a71official]

what is "mega" a number?????

[@cataminz933]

184711 is a prime number

[@TheBalthassar]

God I hope you've taken the battery out of the remains of that laptop.

[@robertveith6383]

I memorized the two-digit prime numbers, so I don't have a clever way to recognize them.

[@ToxicityLimits]

Why when he speaks it makes sense

[@yasminbegum3507]

Frenzy

[@larswilms8275]

It sounds like a very complicated way to do the erostothenese sieve. But yes it works. There is also a "easy" trick for divisibility by 11. Add the digits of the even places and subtract the odd places digits. if the anwer is 0 or a multiple of 11 than your number is divisible by 11 So 1234567891011 --> 1+3+5+7+9+0+1-2-4-6-8-1-1 = 26 -22 = 4 so not divisible by 11

[@ComboClass]

That 11 trick came up in an earlier episode about palindromic numbers

[@GirishManjunathMusic]

17 is just the worst prime. Absolute house cat of a number.