Absolute Primes - Numberphile

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Absolute Primes are also known as permutable primes and anagrammatic primes (and not yet Jumble Primes). We also discuss Circular Primes.
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[@numberphile]

See brilliant.org/numberphile for Brilliant and 20% off their premium service & 30-day trial (episode sponsor) Patrons can see some behind-the-scenes animation pics... www.patreon.com/posts/112540138

[@MacAlister11]

7wj80

[@Anonymous-df8it]

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

[@dskinner6263]

The animator did such an excellent job of resuscitating my childhood memories of educational television. Sound effects are spot-on too 👍

[@numberphile]

Thanks animator Pete

[@warrensharp6681]

Shout out to animator Pete🙌🙌🙌

[@seventhtenth]

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

[@robinbrowne5419]

Yes. I was just waiting for the Count to start counting.

[@37wheels]

Peak sesame street vibes 😊

[@henryginn7490]

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.

[@JMUDoc]

"... if only there was a test to see if something is divisible by seven..." Tony Padilla: am I a joke to you!?

[@soilnrock1979]

He was actually referring to his own video about "Solving Seven" from two months ago :-)

[@magnus0017]

I mean, to be fair, one way to test it would be dividing it by seven and seeing if there is a remainder.

[@EastBurningRed]

the divisibility by 7 tests have the same computational complexity as just dividing by 7

[@trevinbeattie4888]

“Who knows? Let’s find out!” I love James’ enthusiasm.

[@benpetersjones]

James the @singingbanana talking about primes on Numberphile is my happy place.

[@swankitydankity297]

the animations in this video are really cool

[@bimblinghill]

I hope they're real stop-motion, not digital!

[@GorFrag]

very old school sesame street

[@NabeelFarooqui]

Does it say anywhere who makes them?

[@OutbackCatgirl]

​@@GorFragwow i did not expect to spot a wild dorin in the comments of numberphile! worl smol, number cool

[@commaJim]

You're really cool

[@RichardHolmesSyr]

In binary, the circular primes are the Mersenne primes (and they're all boring).

[@MonsieurBiga]

"Who knows?? I know." 😂

[@WarmongerGandhi]

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.

[@ralphengland8559]

That's what I was thinking.

[@hughcaldwell1034]

Pseudo-boring absolute primes.

[@RichardHolmesSyr]

In bases 11 and 13 there are (3-digit) exceptions.

[@rosiefay7283]

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.

[@RichardHolmesSyr]

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.

[@RichardHolmesSyr]

In prime number bases every digit except 0 is legal, so you get more possibilities and end up with more absolute primes.

[@StephanTrube]

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.

[@asheep7797]

But what if you need a prime that is at least 20 digits, and they can't all be ones? Remember: 12345678910987654321.

[@KitagumaIgen]

@@asheep7797 With my poor short-term memory and generally "bad luck in ironic circumstances" this will not end well...

[@brumd]

Ha, someone is having a blast with his modular synth! :) Always appreciate the tasteful sound fx on Numberphile. O yes, nice video too!

[@johnloony68]

I like the use of the animations instead of just the boring brown paper

[@24c0xy]

733 is an absolute prime and is bigger than 337. James owes me dinner

[@skarfie123]

991 is even bigger

[@HammerShock23]

Went to the comments to see if anyone beat me to it 😂

[@TheMichaelmorad]

the animator here had a lot of fun making this video

[@djsmeguk]

Writing down that number would require more than the number of particles in the universe. I think James' challenge is safe.

[@RichardHolmesSyr]

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...

[@djsmeguk]

@@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.

[@stheil]

Eh sure you can do it in binary too but they'd all be boring repunits. Can't contain even a single 0

[@zinxys]

So , for base 2, it is all the Mersenne primes and nothing more.

[@avi12]

There's something very satisfying in the animation with the sound effects

[@icetruckthrilla]

So is 13 the first non-boring circular prime? Update: it is

[@bjornmu]

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.

[@Anonymous-df8it]

What was the algorithm?

[@sarahdaviscc]

You loved Blue's Clues but have you seen Grime's Primes?

[@WAMTAT]

James Primes is back!

[@JohnPretty1]

Grime numbers.

[@electrikhan7190]

Your block animations on point. 12:39 lies, what you have is worth more than gold.

[@davelennie1591]

Really nice job on the visualizations for this one!

[@yourguard4]

Fun fact: In base-1, every prime is a circular prime. So we can say, atleast there are infinitly many of them.

[@youtubersingingmoments4402]

7:45 "You could do it in binary" and would have the most boring afternoon ever lol.

[@tristancam7219]

In binary: could not contain a 0 so essentially must be primes of the form 2^k - 1 (repunits then)

[@MarkMark]

For James’s sake, I hope there is no infinite numbers of circular primes out there, waiting to be discovered. ;)

[@KarstenJohansson]

2:36 Here is where I ran out of fridge magnet 1's.

[@nhatminhtranngoc8940]

19937 is also picked because it's a Mersenne prime exponent

[@nicksamek12]

I’m surprised the factors you decided for 22,33… I would say 11 :D

[@MisterUnlikely]

There is a reductive test for division by 7. Consider that any z can be written as 10x+y. If z is divisible by 7, 10x+y is divisible by 7, which means that 3x+y is divisible by 7.

[@MrDarkPage]

James grimes made a video about it some time ago, that's why he is joking that there is no way to do it.

[@deliciousrose]

4:35 cheeky reference!

[@toolebukk]

Top notch animations in this!

[@toolebukk]

Anagram Prime crew represent!

[@Sebastian-xb5hj]

I think the rep unit primes are worth keeping in mind, since in binary those would be the only circular primes.

[@yiannchrst]

Someone had fun with the editing on this one!

[@amirilan4435]

Oh boy, starting to look for a big jumble prime right away!

[@skarrambo1]

Went out with this mad lad the other day, honestly, you couldn't factor him away from himself and one if you tried. But even when he was completely out of order, you still couldn't! What an absolute prime lad

[@Seltyk]

Dr. Grime is in his villain arc with all this sarcasm

[@bowboysam]

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?

[@rosiefay7283]

A prime with that property is a Sophie Germain prime. We don't know if there are infinitely many.

[@Musicworld01_]

Prime numbers are my favourite.

[@krupam0]

7:40 Well, I'm glad I watched the video before posting my comment.

[@seventhtenth]

😂

[@kinoseidon]

That pesky ol' 91, trying to trick me into thinking it's prime again...

[@Goldendroid]

It’s always the 7s

[@JohnPretty1]

@@Goldendroid 121 says different.

[@Goldendroid]

@@JohnPretty1 Isn’t that just 11 x 11

[@malvoliosf]

Any binary circular prime would necessarily be a repunit (since there cannot be a zero in it), and therefore equal to 2ⁿ-1 for some n. These are the Mersenne primes. The highest known Mersenne prime is (in binary) 82,589,93 ones in a row.

[@orsonzedd]

Every prime number is an absolute prime there aren't any negative prime numbers

[@Thrna_1]

This is prime content.

[@TooMuchDad]

Really loved the stop motion you did with the number blocks :)

[@numberphile]

Animator Pete McPartlan was the man!

[@GhostyOcean]

Only at the 2 minute mark and I have a few thoughts: 31 and 13 are circular primes No circular prime with more than 1 digit can have an even digit or a 5 digit

[@JaquesCastello]

Fun fact: all circular primes in base 2 are Mersenne primes. And vice-versa.

[@JorjEade]

"I'm confident that 337 is going to be the biggest one" uh.. 733?

[@malvoliosf]

I think the rule is, it is the small value in the permutation set that is used as the name.

[@M4DA.]

Whats interesting and was not mentioned is that there are no "pure" absolute prime numbers. The only absolute primes are those whose available permutations are rotations

[@EternalLoveAnkh]

I'm working on a project now. 337 has another special property. Can you guess? I'll be posting a video soon. RJ

[@cyrilmeynier5688]

a circular prime in binary can not have any "0" in it, because the number would be even when the "0" goes at the end. So a circular prime in base 2 is written only with "ones". it's a repunit in base 2. So it's 2^n-1 with some integer n. but we already know those, those are Mersenne primes.

[@louisreinitz5642]

All of the absolute primes permutation of digits are just part of the circular rotations

[@not2tired]

Wild guess - penabsolute primes (wholes where all but one digital permutation are prime) are scarce beyond just a few digits

[@kantoros]

I sometimes think about this, what's the smallest positive integer where we don't know if its prime or not? simply because no one bothered to check yet

[@glenneric1]

Near the largest found prime but 2 bigger. Maybe

[@gustavoschneider6781]

So, I found that 733 is an absolute prime, and it's bigger than 337, so... do I get a dinner invitation?

[@MrDarkPage]

In base 2: if it contains a 0 then one of the rotation will be divisible by 2, circular prime mersenne prime, and they are all "boring"

[@jeffelkins426]

There has to be a better name for these primes... How about "Optimal Primes"? They transform very well.

[@glenneric1]

Optimus. Love it

[@beardymonger]

Love you content!!!! 1. Personally, I don't like math videos centered on base 10 2. Would like to see a video about what would be the most natural base ,mathematically speaking.

[@wierdalien1]

Why would there be one?

[@nebelung1]

Perhaps binary is the most "natural"... It depends what you mean with natural but it requires the least number of "made up" symbols just 1 and 0.

[@tomholroyd7519]

love the animations

[@fspar]

There is actually an easy test for divisibility by 7! Consider n = 10a + b, if 7 | n, then 7 | a - 2b (that's easy to prove) So for example 537 -> 53 - 2*7 = 39 -> 3 - 9*2 = -15 which is not divisible by 7

[@seventhtenth]

560 - 537 = 23 537 = 7•(80 - 21/7) +2 537 = 7•77 +2

[@nowster]

I was thinking the prize would be a Bounty bar.

[@michaelkindt3288]

I wonder if other base systems have more interesting jumble primes. The fact that the only known ones in base 10 technical are two of the same numbers and then a third different number feels like cheating, because there's no meaningful difference between, say, writing the number backwards and just rotating it. Maybe there's a base system that has jumbled primes with three distinct numbers, that would be neat.

[@MeriaDuck]

The stop-motion team had a lot of fun work 🙂

[@pmcpartlan]

Ha, team! Just me in my shed!

[@wybren]

Base 3 might get you a dinner. It's the first base that has properties that allows for absolute primes and limits the issue base 10 has. Or wait... Maybe base 3 makes things harder because you get more digits for the same number. More digits means more problems. Base 20 might be the answer instead.

[@WK-5775]

The prize is for base 10, I guess.

[@mmburgess11]

I spent the entire video trying to figure out how to name one of those numbers a "Parker" number.....

[@tobiasherbst8894]

4:39 Yeah, real shame about that. Someone should make a video about it. 😂

[@_notch]

Yaaaaaay, Singingbanana!!

[@Leviatan5716]

This is the key to understanding autism, though the way we think

[@keyaanmatin4804]

binary circular primes would be all 1s !

[@hughcaldwell1034]

373 satisfies a fun, useless, and very restrictive property I's contemplating a few weeks ago: all its substrings (3, 7, 37, 73 and itself) are prime. (Yes in base 10, obviously.)

[@rickbezoski682]

I want to find an Absolute Permutational Circular Prime, that completes the Parker Square.

[@rickseiden1]

Jumble Primes would be a good band name!

[@ipranay]

We need dish named “Jumbo Prime”, don’t we?

[@TheRilly]

Wow it is a very good number!

[@swingardium706]

7:45 "you could do this in binary", well you could but if the number has a 0 it automatically gets excluded since at some point that 0 ends up in the 1s position and the number becomes even so any circular primes would have to just be long strings of 1s which is pretty unsatisfying (even though it means that all Mersenne primes are circular in binary)

[@chrsbll]

I'd like to nominate "Shuffle Primes"

[@glenneric1]

Interestingly the number of digits in these primes themselves will probably be prime else you increase the chance that they can be fragmented into identical pieces thereby proving they aren't prime.

[@WK-5775]

You mean the repunit ones, right?

[@sghuisman]

Don't want to dive into another Numberphile challenge, but how would one even do primality testing on numbers of magnitude 10^175?

[@johnloony68]

slowly

[@skyjumper4097]

the thumbnail + 7 seconds into the video there are already a 73 and 37 wha

[@thetinkerist]

I would only humbly ask for fish and chips together, and check one possible number every year, so best to have that fish and chips now before it is unedible. ok?

[@ericmckenny6748]

Uploaded before tea time

[@faenethlorhalien]

Wow... maths get seriously bizarre at times.

[@rmdodsonbills]

I don't see how absolute primes are actually different from circular primes. Since the ones we know about all have multiple copies of one digit, jumbling them out of rotation doesn't give us a different list of permutations, just like the two digit primes that we denounced as boring. Or put another way, we said the two digit ones were boring because there wasn't any other way to jumble them besides the rotation and the same is true of the three digit ones we found. Since there isn't any difference between the two threes in 337, swapping them is out of rotation, but it's the same number.

[@WK-5775]

No. 197, 719, 971 are circular, but not absolute primes. Moreover, this is just the situation for base 10. For other bases, things might be different.

[@MindstabThrull]

Imagine if (googolplex squared)-3 was a jumble prime :D

[@yoram_snir]

How did that dinner prize was squeezed 🎉

[@Codricmon]

If we assume this theoretical number has _exactly_ 6*10^175 digits, can only consist of two different digits, and those digits are limited to 1, 3, 7 and 9, then there's only twelve possible forms this number can take. Actually, since we have 6*10^174 instances of a, and 6*10^174 is necessarily a multiple of 3, then b cannot be 3 or 9, since then the number itself would be divisible by 3. This removes half of the possible combinations, leaving only six. That's as far as I go, the rest should be trivial, really. If you manage to find the number after reading this comment, I expect to receive part of the price... Just send a chicken nugget and a half-hearted greeting from James my way or something.

[@alistairkentucky-david9344]

Last time I was this early we didn't even know whether there were infinitely many primes.

[@AnAverageItalian]

Euclid what you doin here go back to Athens 💀💀💀

[@ilovecats_og]

12:58 991, there you go

[@JohnPretty1]

I thought you would offer your house or something James!

[@penfold-55]

Is "absolute prime" a property of a number or is this something only in base 10? My intuition is that it is not a property of a number. My intuition says that base 2 ruins most of this

[@emiltonklinga3035]

9:43 Those 3-digit primes are also boring since they have no more permutations than the rotations.

[@lockedcow727]

Since the 3 digit absolute primes have a repeating digit, they are boring as well. All the distinct permutations are cyclic

[@sirmanki]

It's always a joy to see Dr Grime in a numberphile video!

[@dliessmgg]

One way to see circular primes is: The digits are arranged on a circle. You can start at any digit and go in clockwise direction, and you get a prime. So I'm proposing bicircular primes: The digits are arranged on a circle. You can start at any digit and go in either direction, and you get a prime.

[@MooImABunny]

rep-unit primes are most interesting in binary, so much so, that they have a name - the Mersenne primes. Other than that, the only other digit we have is 0, so we're stuck - there are no 'interesting' circular primes in binary