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4:36-4:41 "If only we had a test to work out if 91 was divisible by 7, but there isn't one, so we'll move on." Take the last digit, then subtract it from the rest of the number. The resulting number is divisible by seven if and only if the original number is
Starting the video off with a number, explaining how it satisfies some property that is almost certainly uesless, and James Grime with his unbounded enthusiasm... this is the classic numberphile content I love. Animations were especially nice this time as well.
@@vibaj16 Well, it is... in base 3. 1 * 3^1 + 2 * 3^0 = 5 (prime) and 2 * 3^1 + 1 * 3^0 = 7 (prime). 😁 In my defence, the whole idea is nuts, so changing bases for extra laughs seems well in order!
There are no circular primes, only repunits. A binary circular prime would contain a zero, and when you rotated that to the units position it would be divisible by 2.
Sort of mentioned in the video, but the 3 listed "non-boring" jumble primes are actually "boring" as well. They are of the form ABB, so their permutations are equivalent to the cycles. So there is no non-boring jumble prime.
@@konuralpyldzkan1495 197 is a prime but not a jumble/absolute prime because 719=7*113 isn't prime, and 917=7*131 isn't prime. They specified all the base-ten absolute primes in the video.
@@scottclowe by definition, all jumble primes must be circular. If all permutations of the number are prime, then that includes all of the cycles as well, so it's not surprising at all. If you meant that all jumble primes are of a form where all permutations are a part of the cycle, then that's actually not surprising either. Otherwise the list of circular primes would have to contain entries that were permutations of eachother. For example, if 197 was a jumble prime, then 179 would have needed to be a circle prime as well. Or for 3779 to be a jumble prime, then 3797 and 3977 would both need to be circle primes. Basically, because none of the circle primes are permutations of eachother (outside of their own cycles) means that the only jumble primes are those whose cycles contain all of their permutations.
In binary, all circular primes will be repunits, because rotating a 0 to the end would give you an even number. And since repunits in binary are all of the form 2^n-1, the circular primes in binary are just the Mersenne primes
Numberphile, I am working on my (currently amateur) master’s thesis in abstract mathematics, and you have taught me so much I would have never been able to even concieve had I not found your channel. I absolutely ❤❤❤ your channel, your videos are 5⭐️⭐️⭐️⭐️⭐️
My favorite thing about 1111111111111111111 is that if we treat it as a binary expression and convert it to base 10, it becomes 524287... which is also prime.
I like "the first non-obvious composite" as the name for 91. It's actually a pretty brief proof: any multiple of 2, 3, 5, or 11 will look composite, as will squares. So the smallest non-obvious composite must be 7*13, which is 91.
1:02 Thank you for acknowledging this early. I find it frustrating when something is base-specific without it ever being mentioned, as it can mislead people into seeing a pattern where it is really just a coincidence based on an arbitrary choice.
I checked bases 2 through 16 going up to 6 digits and found just four absolute primes that have more than two different digits (and therefore include more permutations than circular shifts): In base 11: 139 and 36a; in base 13: 247 and 78a. Many bases have absolute primes that are longer than 3 digits and are not repunits (but are "near-repunits"): for instance 7777d base 15. But not in base 10.
By my logic the higher the base while being prime number the more absolute primes. I'd bet that base 17 and base 19 have at least 2 each absolute primes with at least 3 different digits, maybe even 4 different digits one is on the cards.
@@tadeuszkubera3060 I'll take that bet (now that I've checked...) In base 17 I find no non-repunit absolute primes higher than 6ddd and none at all with 3 different digits. Base 19 has just 29e with 3 different digits, and none above 2ddd. Base 23 has 49i and 6ef but no others with 3 different digits, and no non repunit absolute primes above biii. Through base 31, the only ones of these "very absolute primes" as we might as well call them are 3 digits, of which base 29 has 5.
1.....1 with 19 digits is a prime? How cool! Will try to remember that just in case, if I ever need a fairly big prime number in a life or death situation.
Yes this was supposed to be a joke! TL;DR: write n={a}b where b is the last digit and {a} is all the rest. Then n mod 7 = (a-2b) mod 7. So with 91, 9-2.1=7 so 91 is divisible by 7 💚
Thank you for the video! I just wanted to say that whoever did the thumbnail for this video is brilliant - I instantly understood the premise despite not having heard of this concept before.
Writing it as a sequence of digits, sure, but you can also write it as just the two distinct digits plus the total number of times you use the first digit (which is something like a 175 digit number), so specifying such a number is easily possible. Testing the primality is another matter...
@@RichardHolmesSyr Testing primality would likely require the full representation in some form. Also, you'd need to keep track of each of the positions of the b digit once checked for primality. Which would require the same number of states as digit count. Computationally extremely challenging for sure.
Now there's a surprise, Primed (!) by your video's title, I thought that 19937 would be special because it's the exponent of a Mersenne prime --- indeed, the prime that is the basis of the Mersenne Twister. Didn't know this additional property of 19937.
In binary, the only circular primes are rep-units. Rep-unit primes in binary are Mersenne Primes. There are infinitely many circular primes in binary if and only if there are infinitely many Mersenne Primes.
I actually referred to the number 19937 at work this week, 😁I found that a program crashed because it tried to allocate 19937 bits in a place where this was too much. This is used in a pseudo number generator based on the fact that 2^19937-1 is a prime.
Ha, someone is having a blast with his modular synth! :) Always appreciate the tasteful sound fx on Numberphile. Wild guess: I hear monophonic analog sounds, with some wavefolding here and there, filtersweeps and lots of S&H going on. I wouldn't be surprised if all sounds come from Make Noise's 0-Coast. But of course, I could be entirely wrong.. O yes, nice video too!
There is a test for divisibilty by 7. Let n = 10 a + b; h = 2. If 7 | a - hb, then 7 | n. In our case: 91 = 10 x 9 + 1; 9 - 2 x 1 = 7; 7 | 7. This is easily generalised: (10, m) = 1 10h ≡ 1 (mod m) 10a + b ≡ 0 (mod m) h(10a + b) = 10ah + bh ≡ a + hb (mod m). Take m = 7: 10h ≡ 1 (mod 7) h ≡ 5 ≡ -2 (mod 7).
There are no rotating primes in binary other than rep primes. Any binary number is made up of 0s and 1s. Any binary number beginning with a 0 is even. So any prime with a 0 in it cannot be a rotating prime because the 0 would work its way to the first digit and make the number even. So rotating primes in binary can only have 1s in them, which makes them rep primes.
Props to animator Pete for the brilliant animation! It feels like watching an educational show on CBeebies. Sound effects are spot on too. Thank you Numberphile for enabling my love of prime numbers :D
Excellent video as always. Although I'm a little sad that they didn't explicitly mention the emirps. (Those primes which, when their digits are reversed, result in a number that is also a prime). For two digits - The emirps are synonymous with circular primes and absolute primes. 13&31, 17&71, 37&73.. For three or more digits the emirp definition is less restrictive than circular primes and absolute primes.
If all of the absolute primes have to be of the form aaa...ab, they're all kind of "uninteresting" in the sense that all of the permutations will be identical to one of the rotations.
If I couldn’t speak a human language, I still just think listening to Dr grimes and Brady would be as soothing as non random white noise… this is what should have gone out in the anti-fermi paradox satellite
10:42 a repeated digit in a three digit circle prime, makes the circle and jumble comparison the same. So, if we define a non-trivial jumble prime as a prime with the digits in any order that has an order of digits that is not in the circular prime, then there are NO known non-trivial jumble primes in base ten. And the LaGrou-Conjecture of jumble primes is that there are NO non trivial jumble primes. !
I thought an interesting fact that wasn't mentioned in the video (unless I missed it) is that for these larger numbers, there must be at least one 1 or 7 digit, because all the numbers that are only composed of 3s and 9s are divisible by 3.
One thing I really like about this is that it neatly explains how we imagine a number in base-10 might be prime. It explains the intuition that such a number should have a lot of odd digits, and that it should have a 1 or a 7 in it. In other words, if you ask me to give you a 5-digit number that might be prime I think this is the intuition I will try to employ.
I wonder if anyone realises that the question of "are there infinitely many circular primes?" reduces to the more well-known question of "are there infinitely many Mersenne primes?" when you're working in base 2.
I was wondering whether there are "interesting" absolute prime in other bases, and wasn't disapointed, there are a lot of absolute prime with 3 distinct digit in other bases, some of them are absolute prime in more than one base, for example (chosen few,, because there really are a lot of them): 769 is an absolute prime in bases {11: '6-3-10', 13: '4-7-2'} 1489 is an absolute prime in bases {13: '8-10-7', 29: '1-22-10'} 10069 is an absolute prime in bases {25: '16-2-19', 91: '1-19-59', 94: '1-13-11'} 15277 is an absolute prime in bases {25: '24-11-2', 31: '15-27-25', 79: '2-35-30'} 79669 is an absolute prime in bases {118: '5-85-19', 131: '4-84-21', 211: '1-166-122', 256: '1-55-53'} I haven't yet found an example of an absolute prime with 4 distinct digits in any bases (or even when I allow one repeated digit)
There is a test for multiples of 7: you can subtract any digit, and double that digit from the next digit to the left. If that is a multiple of 7 then so is the original number. With 91 you subtract the 1 from the ones, and doubling that subtract 2 from the tens, leaving 70, which of course is a multiple of 7.
I wonder how many more prime videos Brady and Dr James Prime... er, Dr James Grime... can come up with. I would definitely be interested in a video or series of videos that explores the properties of primes in other bases, as in what they look like, etc... there may even be some clues to the Riemann Hypothesis hiding in there... but probably not, because I'm sure mathematicians have explored this in depth already.
A suggestion for a future video I would love for you guys is to go in to the topic of long scale vs short scale maths and why different countries use them. Million/milliard, billion/billiard and trillion/trilliard vs million, billion and trillion.
Can you tell me what is the biggest prime number that when doubled + 1 gives another prime number, or is there no limit.? Eg 11x2+1=23….23x2+1=47 is there a super-huge mega prime out there when doubled+1 will give an humongous prime?
Pete McPartlan great animation and sound effects! Is this actually stop motion or completely digital and made to look like stop motion? Regardless, it's a great touch. Cheers!
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7wj80
4:36-4:41 "If only we had a test to work out if 91 was divisible by 7, but there isn't one, so we'll move on." Take the last digit, then subtract it from the rest of the number. The resulting number is divisible by seven if and only if the original number is
What of 107?
071
@@CatherineJessicaNatof what of 710?
991. I win.
The animator did such an excellent job of resuscitating my childhood memories of educational television. Sound effects are spot-on too 👍
Thanks animator Pete
Shout out to animator Pete🙌🙌🙌
the visual aid would be nice for calculus or diff eq, but for number theory without notation? distracting for a simple number theory video imo
Yes. I was just waiting for the Count to start counting.
Peak sesame street vibes 😊
Starting the video off with a number, explaining how it satisfies some property that is almost certainly uesless, and James Grime with his unbounded enthusiasm... this is the classic numberphile content I love. Animations were especially nice this time as well.
Agree. The claymation was slick
I don't know about useless. It brings up questions about the the entire structure of mathematics
@@furnacego2164Agreed, if somebody gets interested in math more generally because of this property, then it’s not useless
37 is the 12th prime and its circular prime 73 is the 21st prime
This is the kind of information I came here for 😃😃
the most absolute absolute prime
@@konuralpyldzkan1495 if only 12 was a circular prime
Cool - and absolutely useless 🤓
@@vibaj16 Well, it is... in base 3. 1 * 3^1 + 2 * 3^0 = 5 (prime) and 2 * 3^1 + 1 * 3^0 = 7 (prime). 😁
In my defence, the whole idea is nuts, so changing bases for extra laughs seems well in order!
In binary, the circular primes are the Mersenne primes (and they're all boring).
And in binary the repunit primes are also the Mersenne primes...
Was about to comment the same thing!
1111111111111111111 is my favorite prime ^^
Yeah, repunits are trivial as circular primes no matter the base.
There are no circular primes, only repunits. A binary circular prime would contain a zero, and when you rotated that to the units position it would be divisible by 2.
Sort of mentioned in the video, but the 3 listed "non-boring" jumble primes are actually "boring" as well. They are of the form ABB, so their permutations are equivalent to the cycles. So there is no non-boring jumble prime.
Yes, I was surprised that all base-ten jumble primes are [merely] cyclic primes!
I was coming down here to say the same thing.
there is 197
@@konuralpyldzkan1495 197 is a prime but not a jumble/absolute prime because 719=7*113 isn't prime, and 917=7*131 isn't prime. They specified all the base-ten absolute primes in the video.
@@scottclowe by definition, all jumble primes must be circular. If all permutations of the number are prime, then that includes all of the cycles as well, so it's not surprising at all.
If you meant that all jumble primes are of a form where all permutations are a part of the cycle, then that's actually not surprising either. Otherwise the list of circular primes would have to contain entries that were permutations of eachother. For example, if 197 was a jumble prime, then 179 would have needed to be a circle prime as well. Or for 3779 to be a jumble prime, then 3797 and 3977 would both need to be circle primes. Basically, because none of the circle primes are permutations of eachother (outside of their own cycles) means that the only jumble primes are those whose cycles contain all of their permutations.
In binary, all circular primes will be repunits, because rotating a 0 to the end would give you an even number. And since repunits in binary are all of the form 2^n-1, the circular primes in binary are just the Mersenne primes
such a smart observation, was thinking about how this would work on binary as well lol :)
That can't be right. All repunits in binary are divisible by 3, therefore cannot be primes.
Numberphile, I am working on my (currently amateur) master’s thesis in abstract mathematics, and you have taught me so much I would have never been able to even concieve had I not found your channel. I absolutely ❤❤❤ your channel, your videos are 5⭐️⭐️⭐️⭐️⭐️
My favorite thing about 1111111111111111111 is that if we treat it as a binary expression and convert it to base 10, it becomes 524287... which is also prime.
you mean binary?
That is a fun fact!
They are Mersen primes
2^23-1 edit can you see Krishna Sayee rules number that’s me who s there and thanks for 2likes
@@drggayathridevi195 I'm sad that this video didn't explain Mersenne primes and explain whether we know if they are infinite.
We've gotten James so much recently, that it almost feels normal again! Yay, still glad to have James back!
The Parker "Cicular" Prime: a prime that is almost circular except for one composite form.
Damn, you beat me to it.
Same 😂😂😂
I'll name one: 29
you misspelled circular
You loved Blue's Clues but have you seen Grime's Primes?
“Who knows? Let’s find out!” I love James’ enthusiasm.
"I know!"
Este concepto de primos absolutos solo funciona en la base decimal. Para otras bases numéricas, simplemente se aplican otras reglas.
"Mister Owl, how many licks does it take to get to the Tootsie Roll center of a Tootsie Pop?" "Let's find out. One.... two... three . Three"
@@ultracreador They did make that clear in the video.
I love the old-school stop-motion animations. Perfect.
John Conway has a famous “proof” that 91 is the first composite number that looks prime.
I like "the first non-obvious composite" as the name for 91. It's actually a pretty brief proof: any multiple of 2, 3, 5, or 11 will look composite, as will squares. So the smallest non-obvious composite must be 7*13, which is 91.
I first saw it in a lecture he gave about FRACTRAN.
And Grothendieck has a famous counterexample!
@@Jeff_Saunders Of course! 57, right?
@@trimeta It's neat when someone has the kind of brain that can work backwards to figure out why something 'feels' correct, even when it isn't.
1:02 Thank you for acknowledging this early. I find it frustrating when something is base-specific without it ever being mentioned, as it can mislead people into seeing a pattern where it is really just a coincidence based on an arbitrary choice.
Yeah. People using base 10 especially have this bad habit not mentioining the base.
Interestingly enough, It would be impossible to have non-repunit circular primes in base 2.
Really loved the stop motion you did with the number blocks :)
Animator Pete McPartlan was the man!
James the @singingbanana talking about primes on Numberphile is my happy place.
the animations in this video are really cool
I hope they're real stop-motion, not digital!
very old school sesame street
Does it say anywhere who makes them?
@@GorFragwow i did not expect to spot a wild dorin in the comments of numberphile! worl smol, number cool
You're really cool
I checked bases 2 through 16 going up to 6 digits and found just four absolute primes that have more than two different digits (and therefore include more permutations than circular shifts): In base 11: 139 and 36a; in base 13: 247 and 78a.
Many bases have absolute primes that are longer than 3 digits and are not repunits (but are "near-repunits"): for instance 7777d base 15. But not in base 10.
In prime number bases every digit except 0 is legal, so you get more possibilities and end up with more absolute primes.
By my logic the higher the base while being prime number the more absolute primes. I'd bet that base 17 and base 19 have at least 2 each absolute primes with at least 3 different digits, maybe even 4 different digits one is on the cards.
@@tadeuszkubera3060 I'll take that bet (now that I've checked...) In base 17 I find no non-repunit absolute primes higher than 6ddd and none at all with 3 different digits. Base 19 has just 29e with 3 different digits, and none above 2ddd.
Base 23 has 49i and 6ef but no others with 3 different digits, and no non repunit absolute primes above biii.
Through base 31, the only ones of these "very absolute primes" as we might as well call them are 3 digits, of which base 29 has 5.
You can have more permutations than circular shifts even with 2 digits. Example a number of form ABAB. Any absolute primes like that?
i just love this dude's way of explaining things, simple and clear- sign of a great mind imo
i love how much effort the animator went into the animations!
1.....1 with 19 digits is a prime? How cool! Will try to remember that just in case, if I ever need a fairly big prime number in a life or death situation.
But what if you need a prime that is at least 20 digits, and they can't all be ones?
Remember:
12345678910987654321.
@@asheep7797 With my poor short-term memory and generally "bad luck in ironic circumstances" this will not end well...
@@asheep7797excellent choice for a password that hackers would never guess😅
I will add this to the list of ways that James Bond will not meet his end!
Belphegor's Prime: 1000000000000066600000000000001
A palindromic prime with 31 digits!
"... if only there was a test to see if something is divisible by seven..."
Tony Padilla: am I a joke to you!?
He was actually referring to his own video about "Solving Seven" from two months ago :-)
I mean, to be fair, one way to test it would be dividing it by seven and seeing if there is a remainder.
the divisibility by 7 tests have the same computational complexity as just dividing by 7
@@EastBurningRed True, but they generally require less thought for a human being.
Yes this was supposed to be a joke! TL;DR: write n={a}b where b is the last digit and {a} is all the rest. Then n mod 7 = (a-2b) mod 7. So with 91, 9-2.1=7 so 91 is divisible by 7 💚
Thank you for the video! I just wanted to say that whoever did the thumbnail for this video is brilliant - I instantly understood the premise despite not having heard of this concept before.
I insist that all future numberphile videos display any number animations via number blocks. I loved it!
I've been watching this channel for 8-10 odd years and James Grime hasn't aged a day nor lost any of his energy. Buddy is a beaut
Pete McPartlan do be cooking with these animations 🔥🔥🔥
He was so confident there wouldn't be a bigger absolute prime until the idea of having dinner with the nerd who finds it came up
There's something very satisfying in the animation with the sound effects
I absolutely agree that "jumble prime" is a better term for this than "absolute prime".
I agree. :)
the animator here had a lot of fun making this video
Writing down that number would require more than the number of particles in the universe. I think James' challenge is safe.
Writing it as a sequence of digits, sure, but you can also write it as just the two distinct digits plus the total number of times you use the first digit (which is something like a 175 digit number), so specifying such a number is easily possible. Testing the primality is another matter...
@@RichardHolmesSyr Testing primality would likely require the full representation in some form. Also, you'd need to keep track of each of the positions of the b digit once checked for primality. Which would require the same number of states as digit count. Computationally extremely challenging for sure.
Now there's a surprise, Primed (!) by your video's title, I thought that 19937 would be special because it's the exponent of a Mersenne prime --- indeed, the prime that is the basis of the Mersenne Twister. Didn't know this additional property of 19937.
woah cool!
in particular, mersenne primes are just base 2 repunit primes and hence also circular and absolute
"Who knows?? I know." 😂
Plot twist: he didn't know
In binary, the only circular primes are rep-units. Rep-unit primes in binary are Mersenne Primes. There are infinitely many circular primes in binary if and only if there are infinitely many Mersenne Primes.
I actually referred to the number 19937 at work this week, 😁I found that a program crashed because it tried to allocate 19937 bits in a place where this was too much. This is used in a pseudo number generator based on the fact that 2^19937-1 is a prime.
What was the algorithm?
@@Anonymous-df8it It's called Mersenne Twister.
@@Anonymous-df8itMersenne Twister MT19937
@@Anonymous-df8it Mersenne twister!
@@nothayley That's pretty cool about 19937 indeed.
Ha, someone is having a blast with his modular synth! :) Always appreciate the tasteful sound fx on Numberphile.
Wild guess: I hear monophonic analog sounds, with some wavefolding here and there, filtersweeps and lots of S&H going on. I wouldn't be surprised if all sounds come from Make Noise's 0-Coast. But of course, I could be entirely wrong..
O yes, nice video too!
The animations always have new ways of being interesting. Well done!
Eh sure you can do it in binary too but they'd all be boring repunits. Can't contain even a single 0
So , for base 2, it is all the Mersenne primes and nothing more.
There is a test for divisibilty by 7.
Let n = 10 a + b; h = 2. If 7 | a - hb, then 7 | n. In our case: 91 = 10 x 9 + 1; 9 - 2 x 1 = 7; 7 | 7.
This is easily generalised:
(10, m) = 1
10h ≡ 1 (mod m)
10a + b ≡ 0 (mod m)
h(10a + b) = 10ah + bh ≡ a + hb (mod m).
Take m = 7:
10h ≡ 1 (mod 7)
h ≡ 5 ≡ -2 (mod 7).
I’m surprised the factors you decided for 22,33… I would say 11 :D
Big compliments to the animator. It´s so much fun to watch❤
There are no rotating primes in binary other than rep primes. Any binary number is made up of 0s and 1s. Any binary number beginning with a 0 is even. So any prime with a 0 in it cannot be a rotating prime because the 0 would work its way to the first digit and make the number even. So rotating primes in binary can only have 1s in them, which makes them rep primes.
Props to animator Pete for the brilliant animation! It feels like watching an educational show on CBeebies. Sound effects are spot on too.
Thank you Numberphile for enabling my love of prime numbers :D
Always love to see James in these!
1 on 1 dinner with James Grime?! Screw the Riemann hypothesis, this is the NEW chase problem of the 21st century.
Your block animations on point.
12:39 lies, what you have is worth more than gold.
This proves part of my research into primes!!! Thanks so much. Just need help explaining it
Really nice job on the visualizations for this one!
Excellent video as always. Although I'm a little sad that they didn't explicitly mention the emirps. (Those primes which, when their digits are reversed, result in a number that is also a prime). For two digits - The emirps are synonymous with circular primes and absolute primes. 13&31, 17&71, 37&73.. For three or more digits the emirp definition is less restrictive than circular primes and absolute primes.
Top notch animations in this!
If all of the absolute primes have to be of the form aaa...ab, they're all kind of "uninteresting" in the sense that all of the permutations will be identical to one of the rotations.
That's what I was thinking.
Pseudo-boring absolute primes.
In bases 11 and 13 there are (3-digit) exceptions.
Which was already mentioned in the video.
Is the flight to the dinner is paid too in the bounty?
What an awesome animation is that! Looks like it's a photo stop motion
9:43 Those 3-digit primes are also boring since they have no more permutations than the rotations.
So they must be the same!
They address this in the video. Love people that comment trying to prove something before the video is done, lol
@@cgduude Yeah, I didn't watch until the end. Like the primes the video also got boring 😏
9:48 I was *_LITERALLY_* about to comment *_THE SAME EXACT_* thing 😅.
So is 13 the first non-boring circular prime? Update: it is
The real question is where is James hiding the fountain of youth
This is so neat! I'm not really great at math in general, but this channel has shown me how interesting prime numbers are!
Amazing sound effects work!
If I couldn’t speak a human language, I still just think listening to Dr grimes and Brady would be as soothing as non random white noise… this is what should have gone out in the anti-fermi paradox satellite
I like the stop motion animations. Was that a lot of work?
10:42 a repeated digit in a three digit circle prime, makes the circle and jumble comparison the same. So, if we define a non-trivial jumble prime as a prime with the digits in any order that has an order of digits that is not in the circular prime, then there are NO known non-trivial jumble primes in base ten. And the LaGrou-Conjecture of jumble primes is that there are NO non trivial jumble primes. !
In base 10
12:05 ug, I guess my conjecture has already been proven. 😢
I thought an interesting fact that wasn't mentioned in the video (unless I missed it) is that for these larger numbers, there must be at least one 1 or 7 digit, because all the numbers that are only composed of 3s and 9s are divisible by 3.
James Primes is back!
I love those animations!
Dinner with Dr. Games Grime?! Now I wish I had studied more in school!
The animator didn't need to go this hard, but he did!
One thing I really like about this is that it neatly explains how we imagine a number in base-10 might be prime. It explains the intuition that such a number should have a lot of odd digits, and that it should have a 1 or a 7 in it. In other words, if you ask me to give you a 5-digit number that might be prime I think this is the intuition I will try to employ.
2:36 Here is where I ran out of fridge magnet 1's.
7:40 Well, I'm glad I watched the video before posting my comment.
😂
I wonder if anyone realises that the question of "are there infinitely many circular primes?" reduces to the more well-known question of "are there infinitely many Mersenne primes?" when you're working in base 2.
Yaaaaaay, Singingbanana!!
8177207 ones is currently the largest known repunit (probable) prime.
In binary: could not contain a 0 so essentially must be primes of the form 2^k - 1 (repunits then)
Dr Grime is extra sassy today. Love it.
What about palindromic primes? There should be more of those.
I love Dr. James Grime! ❤
God bless him..
I've been playing _Voices of the Void_ and that little wooden maquette on the bookshelf behind Dr. Grime heckin' jump scared me.
I love Frost's commentary but it's still fun when he goes ultra brain, giga mode. Another wild run!
Dinner with James Grime? *Starts bounty hunting right away*
Oh boy, starting to look for a big jumble prime right away!
7:45 "You could do it in binary" and would have the most boring afternoon ever lol.
I was wondering whether there are "interesting" absolute prime in other bases, and wasn't disapointed, there are a lot of absolute prime with 3 distinct digit in other bases, some of them are absolute prime in more than one base, for example (chosen few,, because there really are a lot of them):
769 is an absolute prime in bases {11: '6-3-10', 13: '4-7-2'}
1489 is an absolute prime in bases {13: '8-10-7', 29: '1-22-10'}
10069 is an absolute prime in bases {25: '16-2-19', 91: '1-19-59', 94: '1-13-11'}
15277 is an absolute prime in bases {25: '24-11-2', 31: '15-27-25', 79: '2-35-30'}
79669 is an absolute prime in bases {118: '5-85-19', 131: '4-84-21', 211: '1-166-122', 256: '1-55-53'}
I haven't yet found an example of an absolute prime with 4 distinct digits in any bases (or even when I allow one repeated digit)
a true rotational prime, a rotational prime that can be rotated back to the same number a rotational prime amount of times
There is a test for multiples of 7: you can subtract any digit, and double that digit from the next digit to the left. If that is a multiple of 7 then so is the original number. With 91 you subtract the 1 from the ones, and doubling that subtract 2 from the tens, leaving 70, which of course is a multiple of 7.
This is prime content.
733 is an absolute prime and is bigger than 337.
James owes me dinner
991 is even bigger
Went to the comments to see if anyone beat me to it 😂
he says that in the video...
@AkiSan0 yeah but he in the end made an absolute sbomination of a mistake to say 337/733 and not 991
If you asked me to name a "really big" number before I discovered Maths TH-cam I'd have said, like... a billion?
Can't wait to have dinner with James:)
I wonder how many more prime videos Brady and Dr James Prime... er, Dr James Grime... can come up with. I would definitely be interested in a video or series of videos that explores the properties of primes in other bases, as in what they look like, etc... there may even be some clues to the Riemann Hypothesis hiding in there... but probably not, because I'm sure mathematicians have explored this in depth already.
A suggestion for a future video I would love for you guys is to go in to the topic of long scale vs short scale maths and why different countries use them. Million/milliard, billion/billiard and trillion/trilliard vs million, billion and trillion.
How come every circular prime with odd amount of digits also has their sum equal to a prime number?
I was expecting James to say "The price for finding a bigger absolute prime would be 337 pounds."
Brilliant explanation Of prime numbers!!
Can you tell me what is the biggest prime number that when doubled + 1 gives another prime number, or is there no limit.? Eg 11x2+1=23….23x2+1=47 is there a super-huge mega prime out there when doubled+1 will give an humongous prime?
A prime with that property is a Sophie Germain prime. We don't know if there are infinitely many.
I like the old school stop motion.
Pete McPartlan great animation and sound effects! Is this actually stop motion or completely digital and made to look like stop motion? Regardless, it's a great touch. Cheers!
Thanks! It's proper stop motion the sounds were all done with my modular synth
great sounds effects!
4:35 cheeky reference!
I’m inclined to believe that I would take that dinner over any meagre millennium prize-“millennium prize problem prize?”