Glitch Primes and Cyclops Numbers - Numberphile
ฝัง
- เผยแพร่เมื่อ 6 ธ.ค. 2015
- Audible: www.audible.com/numberphile
More links & stuff in full description below ↓↓↓
Simon Pampena on Glitch Primes and Binary Cyclops Numbers.
Simon on Twitter: / mathemaniac
Some book recommendations... Love & Math by Edward Frenkel, The Simpsons and their Mathematical Secrets by Simon Singh, The Mathematics of Love by Hannah Fry and Alex's Adventures in Numberland by Alex Bellos.
Prime Playlist: bit.ly/primevids
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At the end of this video I should have said that I found that the only cyclops prime in binary is 101. Sometimes when I get excited I lose rigour!
+Simon Pampena Check this out: I found another one
m=2618
(according to Mathematica)
EDIT: In the base ten example of course! So using 10^(2 m) - 10^m - 1
+Omar Z 2^(2 2618+1)-2^2618-1 is not a prime number
+Simon Pampena
9:35
23*59*163*599*75475452511
BacArdI^
I should have specified base ten:
10^(2 m) - 10^m - 1
is a prime for
m=2618
Found another one:
for m=5611
10^(2*5611) - 10^5611 - 1
is prime
Kid : "Mom I need a transformer"
Mom : " We already have one at home "
*Transformer at home* : 1:56
this made my day, hahahahahahaha
Lol 156 likes
Oh my! 🤣🤣🤣
I love you
boring comment!
I was hardboiling eggs and started watching this and forgot to watch the water boil, then when you mentioned eggs it reminded me and the water had just started boiling. Thank you numberphile for saving live on a daily basis
lol
@lightninglynx II late reply
@@kiranaun9593 late reply?
@@natebolan365 latest reply
Joseph Dalrymple latester reply
He drew nines for like 10 minutes while the camera guy just stands there
Someone's got a lot of free time there.
hOI!
HIS NAMES BRADEY GODDAMNIT
Madlad
Donovan Holm calm down lol
"I started doing this at 9pm, I was still doing this at 6am. This is the hole I want to take you down!
that's how mathematicians reproduce
Instead of counting all the freckles on a girl's naked body, math nerds only make a rough estimation.
Like A Snow Monkey In The Night
They also know to get out when there are 0
Read this right as that part came on
“
0:31
The look he gives after writing that ‘8’ is hilarious 😂
I love the quotes in this video.
"that dramatically changed the number of eggs you just bought"
"He's just one of having one of these glitch primes - That would really have made the nerds exited"
+RogerWilco "Swish"
6:55 I started doing this at 9 pm I was still doing this at 6am. This is the hole I want to take you down.
Whereed are the nerds going? Hopefully in the five+ years since your comment you have learned of their destination if you did not know it at the time
It's brilliant how he talks about this stuff like it's the most amazing thing ever
Lobster with Mustard and Rice he's passionate
Mathematics IS the most amazing thing ever, though, right?
The real world doesn’t act like a mathematically perfect universe, where everything has underlying structure that becomes more and more beautiful as your understand increases. Mathematics allows us to access that utopia of order and exactness. What could possibly be more amazing?
@@uniqueusername_
The real world in it's chaotic beauty is more amazing than the strict exactness on paper. The fact that we can model and predict outcomes to an acceptable level is humbling and one of the greatest achievements of man.
It is
when he talks it BECOMES the most amazing thing ever.
What a guy.
+CatnamedMittens “Michael Bialas” The best guy.
He sure is a guy.
+CatnamedMittens “Michael Bialas” My mind has never been blowed so hard.
+Michael van Rhee That accent is really sick, not going to lie.
+Ted Chirvasiu He's definitely a character.
2015 is 11111011111 in binary... So is it a glitch year?
+Speedyjens Its a cyclops year!
+Speedyjens A cyclops year. The Year of the Cyclops.
+Speedyjens nice!
+Speedyjens sure feels like it... sigh**
yeah, but it's not a prime number
I love how he uses a red marker and draws slowly to clarify the 8
The thing you got to love about Simon is how much he commits to the bit. You can tell he gets a hella kick out of writing that absurd number down.
Now we are going to start "The Binary Cyclops Prime" class 101.
That is it.
Thank you for coming, See you later
André Benites
See you April 20th
Work hard revise properly for the exam, and you have a chance to passe this class.
11011
1110111
111101111
11111011111
1111110111111
111111101111111
11111111011111111
Cool boss name
@@gabrielkellar1935 all the numbers you suggested can be divided by either 11 or 111 or 1111 and so on so the only cyclops prime is 101.
1:56 so this is where Transformers got their sound effects :DDDDDD
That would be Glitchimus Prime?
I mean, I needed to actually go
TCHTCHTCHCTCHT
DUGUDUGUDGUU
:]
They are called prime numbers...
Optimua prime...
And he said transform...
Transformers...
Wait what
@@blue9139 So instead of glitch primes, perhaps we should call them Decepticon Primes. A fitting name because they're deceiving us by being so close to a repdigit.
9:33 That "Come on. Swish" killed me. So funny
Why does it make me happy to learn you solved such a meaningless, non-applicable problem?
Probably the same reason I'm subscribed to a channel that's all about numbers.
Bravo, sir.
It's removing a whole class of numbers from prime sieve ? ( it's easy to detect these )
He means non-applicable to the real world
101 likes😂
It is totally applicable. Engineers look to mathematicians for applicable solutions, the math must exist before it can be applied to physical systems.
He's looking for a way to detect primes, but actually.... He just found a few funny numbers.
I guess the binary cyclops numbers can be skipped, so that'll save you 1 every power of 2... which is a quite small number 😅 but I suppose as they get larger, that's significant as anything to be able to skip 1.
His face at 0:32.
"Haaaaa, you didn't expect that one huuuh?"
he's so precious
This guys mind reminds me of how I looked at the world when I was little. Full of enthusiasm
+Tharsshanan2 There is a book that can help you achieve that enthusiasm, it is called the Bible.
+Ar Ky You're ruining mathematics right now.
+Ar Ky Aw man, I respect your right to that opinion, but I personally would say that'd be the LAST book a person should look at for enthusiasm. Any half-decent science text would be a much, much better place to look.
+Ar Ky a truth full of lies? Or whatever you would call inaccuracies and contradictions
Quinn Valor
You need to show proof for your statements.
mentioning Ali G in a video about maths..... this guys the best XD
"This is the sorta stuff you communicate with aliens about"
Thanks for the beginner's course in glitch primes. Glitch primes 101, you might say.
LOL I love Brady's eggs input!
why is vsauce wearing a curly wig?
SAIL THE SHIPS!
Coodles Parks um that's not michel
HEY GUYS. Michael here
he sorta looks like a mix of keemstar, matthew santoro, and bob ross.
We don't call them glitches. We call them happy little accidents.
"this is the sort of stuff you communicate with aliens about, you know what I mean?"
video length is 13:31 which 1331 is 11 cubed. maths is everywhere
Ramanujan would love this video
And 11 is prime!
13 and 31 are primes!
could we find other mirror primes?
like 17 and 71
poeple commenting stuff about a 13 min video... that was published 5 mins ago?
+Jesus Christ sometimes I wish youtube added a feature, that showed the time-stamp of the video at the time the comment was sent... there would be a lot of 0:00 comments out there...
+liquidminds That would add a lot of pointless noise.
Not to mention it wouldn't be very accurate. Have you never returned to a video because someone responded to a comment you left?
+liquidminds but what if you watched the video yesterday and come back today to comment, pause at 0:00 and post your comment :D
Jesus Christ thats fast
TheMasterJoni bad luck :-)
4:09 he went from laughing to extreme serious 😆
Learning with Pibby as reference
Pampena's videos are truly A MUST to watch . He is amazing in explaining . I am really in love with his videos on the legend of question six and transcendental numbers .
What about "10001" type binary numbers?
EDIT: I'm talking about numbers that start with a 1, end with a 1, and only have 0's inbetween.
+Evdog Music this is basically just 2^n +1
and there are many primes with this shape
for example 17 and 257 and 65537...
+Evdog Music That would be a Mersenne Prime.
Sigmath Bits Mersenne Prime is 2^n- 1
his question is 2^n +1
+Sigmath Bits Mersenne Primes are in the 11111111111111111111111111111111 shape
+Evdog Music that's not a cyclops number. cyclops numbers only have one 0.
Wouldn't the square root of -1 be a cyclops number?
How?
i
It has one i
+Mikkel Laursen Because it's only got one i
+Mikkel Laursen that's an imaginary number, so "i" which has one "eye", like cyclops.
+Peregrine M good one
I love numberphile. I appreciate the explanations of high level math concepts, even if I don't always understand (I majored in music). But most of all, I love their passion for the subjects they explain. It's infectious.
Simon is still my favourite guest you've ever had on.
That is an elegant way to demonstrate that 101 is the only Cyclops number, but I was also hoping for an elegant way to deal with the ...99899... number.
Physics Videos by Eugene Khutoryansky :]
I love your videos!!!
The cyclops trick only works if the "glitch" is a zero. If it's not, there are three parts instead of two.
A déjà vu is usually a glitch in the Matrix. It happens when they change something.
+Sniggins I haven't seen it.
+The Hoax Hotel lol
+Sniggins You must be fun at parties.
Yes, but remember how many times the number 101 appears in The Matrix.
+The Hoax Hotel A déja vue in the matrix is not the way we perceive it in real life. When we have a déja vu, we feel like we've done it before. We don't see it twice like the Matrix.
I was expecting a clip of Hitler shouting "NEIN NEIN NEIN NEIN NEIN" to play.
+High Furzi Leader Kitler
so was i, but then again, this is family friendly
+SpaghettiToaster Because he was angry.
***** Idk, man. You just said that there was no such video, and then I showed you such video. My work here is done.
Calm down ladies!
woulda been classless
9:17 so funny how hard this is.
"1 2 3 4 5 6 7 8 ...
...
...
9 8..."
This is the best guy you have on here
+John Sheard I would not be so sure about that, because James Grime.
+John Sheard I would not be so sure about that, because James Grime.
+MadCodex or the Klein Bottle guy
+Lyndon Hanz Pernites That guys enthusiasm though!
Matt parker is much better
This guy rocks and rolls.
I really did think it was a wig at first though.
Simon's passion makes him such a treat to watch and listen. I'd sit in on your lectures anyday!
So did he just sit there and write all that without saying anything. Cause that is amazing.
ERROR 101
GLITCH NOT FOUND
Isira Aarewatte I think it’s bcoz 101 is a glitch prime
Does he mean the only CYCLOPS glitch prime you can have in binary is 101(at the end of the vid)?
yes
+jonlottgaming Yes!
+Simon Pampena Mersenne Primes are also Glitch Primes in binary? They would be of the form 111...1110 with the last zero being the only glitch
+John Sheard if the last digit is a zero the number can be divided by 10 (2)
+William Pereira Gomes of course, mersenne primes would be all 1's in binary, glitchless rep numbers?
Exultantly: "I'm the only person to have discovered this!"
In a conspiratorial tone: "*I'm not really but that's how I feel about maths*"
I feel his love and wonder for math haha I feel it, what a delightful guy!
He's so cute! I love his excitement for math!
It says 600 Views, 60 likes and 0 Dislikes!!! This looks just satisfyingly clean and i'm sure it's only possible on Numberphile ;-P
+Flying Squirrel *lol* I refreshed and then it said 2.542 views, 254 likes and 2 dislikes... not sure if i can handle this awesomeness XD
+Flying Squirrel They probably just pressed dislike to make sure the button works, because of your comment ;P
I'm so early I better make a joke.
My math grades :C
+Gornius C's aren't that bad
+Oscar Gregeborn Rofl.
+top kek I can top that.
My life.
+Oscar Gregeborn C is actually horrible, it corresponds to about a 60% at the very best in the UK.
+crazygoat85 In the U.S. C is 70%-79%
I actually understood nearly all of this one.
You don’t just simply understand a numberphile video
How does he talk about it so calmly and collected. Like, It is insane how well he is articulating his completely insane thoughts. I'm so impressed. "What a guy".
Wait. You posted this on Twitter?
Twitter has a 140 character limit but this number is 506 digits long? What?
probably an image
+Hatsune Miku Project Diva Kevelinu beacuse of a glitch on twitter
+Hatsune Miku Project Diva Kevelinu write it as power of (;
Fernando Batl I was too lazy to write the full equation, but you got me! :P
Never expected I'd hear an Ali G reference here.
I remember this guy! He came to a Maths Teams Tournament that I was at as a guest speaker earlier this year (in Australia)!
"This is the sort of stuff you communicate with aliens about." Love it!
"This is the hole I want to take you down."
I'm game.
Genuinely laughed out loud 4 times in this video... great stuff! Entertaining and educational, I'm a fan.
In fact, any base-b number consisting (as a concatenation) of n rep-(b - 1)'s, 0, and another n rep-(b - 1)'s in that order (such as 999,909,999 in base ten, where n = 4 in this case) factors as:
b^(2n + 1) - *(b - 1)* b^n - 1 = (b^(n + 1) + 1) (b^n - 1)
(in the example given, the factors were 100,001 and 9,999 neither of which is prime in base ten; in fact they're both multiples of 11: 100,001 = (11)(9,091) while 9,999 = (3^2)(11)(101).)
I've watched MANY mathematical videos, but this guy is VERY good with his communication and explanation to aid the listener.
Excellent video.
Excellent speaker.
Hey Brady, I found another one:
m=2618
I mean using
10^(2 m) - 10^m - 1
+Omar Z I should add that I've been searching up to 5127 for now...
Other commenters have mentioned the same number, but are you sure? That's a ridiculously huge number and I don't believe your primality test is rigorous enough to conclusively prove that it _is_, in fact, a prime number.
Look at the documentation of the method that you're using and whether it's actually _guaranteed_ to work with such huge numbers.
Nixitur PrimeQ[] of Mathematica. Of course you are right and I should've checked better the documentation! From Wolfram's page:
"PrimeQ first tests for divisibility using small primes, then uses the Miller-Rabin strong pseudoprime test base 2 and base 3, and then uses a Lucas test."
It is not guaranteed above 10^16, only suspected. Similarly m=5611 gives a positive. I'm running the test up to 10000 overnight for fun.
+Omar Z I confirm that 10^(2*m)-10^m-1 is a prime for m=2618 and m=5611.
It can be proven using a classical primality test known as "the N+1 test" which can be applied when N+1 has a fully factored divisor F greater than cubic root of N, here we have N+1 = 10^(2*m)-10^m = 10^m(10^m-1) so we can use F=10^m.
+Omar Z Don't use that stuff. Divide it with all integers up to sqrt(self). Brute forcing is for the cool people.
Great video Simon and Brady! I especially liked this one; following Simon's thought process and calculations was very interesting, getting a closer look at how maths is actually done in the real world! :)
It’s really cute how excited you are bravo! I remember when I stayed up all night and “discovered” the relationship between binomial powers and Pascal’s triangle.
by far my favorite numberphile video. great vid!
It's a Parker number.
Dude... Congrats... No more words... You guys make this World better =) i with i had teachers like you, not because of how good you teach but because of how good you make us feel while learning
The same trick also works in base 6: 6^(2x+1)-6^x-1=(2*6^x-1)(3*6^x+1) and we can see that there are no glitch primes of the form 555...5554555...555 in base 6. In fact, in base B+1, there are finitely many primes of the form BBB...BBB(B-1)BBB...BBB if there exists a natural number, n, such that B+1=n(n+1). Let's call b=B+1 for simplicity. Note that the glitch numbers we are looking for are of the form b^(2x+1)-b^x-1=(n*b^x-1)[(n+1)*b^x+1] since n(n+1)=b.
I love how excited he gets and the crazy eyes and then back to 9s I laugh every time lol 👍🏻👍🏻keep up the gr8 work
3:50 Even though it does seem like it would make a "big change" changing one of those numbers. You also gotta realize that the 8 is approx. 253 numbers into the number. Even if you had a number that's 11 digits long, lets say 99999899999. ((10^11 - 1) - 10^5) With the 8 in the middle. changing the 8 to a 9 wouldn't be a very high increase. You're only increasing it by 100,000. 100,000 of 99999899999 is 0.0001000001%
"maybe i was the first person..."
me when i finally solve a problem for my discrete class 😅
This was crazy fun! Love that dude.. great job shooting this vid. Feels like you’re right there w him
Simon Pampena is so enthusiastic, its brilliant! great vid
That gave me goosebumps!! That's amazing!
"This is the hole I wanna take you down" - Simon Pampena 7:00
I really enjoyed this session, great work pals.
That look to camera after writing the 8 is priceless
One day there will be a book called "Glitch Primes 101"
I really enjoy these types of numberphile videos because the maths isn't overly complex. He's using basic algebra, something everyone should've had in school when they were young.
You usually present cool and complex but yet understoodable concepts about mathematics.. But in this video I felt like I was taking part of his thinking about this idea. It was very enjoyable, keep it up.
I really like this guy's vids, his enthusiasm for maths is great to watch :)
Him: is this a prime?
Me: NEIN
"That would have really made the nerds excited"
love the passion man... love it!... more journey stories plz
I love Simon videos! He explores totally "useless" but fascinating topics. I love it!
"This is the hole I want to take you down."
JUST TAKE ME ALREADYYYY
Nein Nein Nein!
Awwww, shuckyducky!
Len
Shuckyducky Quack Quack, in da house.
Love this guy and his love for numbers. He's so excited, it's amazing :D
this guy kills it! best video so far
If this were a course we coulld call it primes 101
@2:54 he misspoke , he said "..this has 506 9s.." but this has 505 9s because there's one 8 and there are 506 digits in it
I'm proud of you
and the world is saved again, we thank you for that
No, that was to factor it as powers of ten. It didn't have an eight until he subtracted the other numbers.
so, 10= 10^1, and 10-1=9, so, the power number is the number of 9s. same with 10^2-1, because 10^2=100 and 100-1=99 and that is the power number, 2 so there are 2 nines. same with 10^506-1.
And there was 506 digits which meant it would be 10^50 *7* -10^253
I like your precisely defined formal method for compacting. 1:52
This was such a beautiful thing to watch. Maths is so amazing
I applied the divisible rule and it was pretty simple
(Not sure about the rules being correct though considering I just googled them)
So would 101101 be a normally sighted prime in binary?
Ausaini17
No because 45
@@thatoneguy9582 1101011 is prime
101101=1001×101 in binary
Really love his method for finding out if a number is prime. First you figure out what the number is as a sum of various powers of ten, then you just eliminate the common denominators in the powers and represent them by algebraic symbols, and as a final step all you have to do is to just put the number into a prime number database and that will tell you if your number was prime or not.
Works every time.
What a journey, thanks for posting!
Did you know that 2015 is 11111011111
Snap. You're right! Fancy!
+Felix Berg This is important!
we'll have to wait 100000 years for the next palindrome. Thank goodness I might still be alive!
+SongSeeker7 2047.
2525shion High Furzi Leader Kitler You guys are derps. SongSeeker7 was saying the number of year in binary! (it's 32 in decimal. 2015+32=2047)
9:37
"C'mon 'swish'"
Awesome, dude! The cyclops thing and your discovery!
I like that your logo appears at the bottom right at time mark 13:14, nice touch.
Ali-G math genius confirmed!
Hey numberphile,
Can you guys do an episode about Emirp numbers? Primes that read backwards are primes as well?
A006567 in OEIS
=Vp
Super, je ne suis pas le seul à me poser des problèmes de ce genre sur l'esthétique des nombres et leur particularité ahah. J'ai vraiment aimé cette vidéo :)
This dude is a hidden treasure in TH-cam