The Most Wanted Prime Number - Numberphile
ฝัง
- เผยแพร่เมื่อ 14 ธ.ค. 2021
- Featuring Neil Sloane.
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Neil Sloane is the founder of The OEIS: oeis.org
More videos with Neil: bit.ly/Sloane_Numberphile
Prime Playlist: bit.ly/PrimePlaylist
Note the 17350-digit prime we feature is more accurately classed as a "probable prime" at this time.
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More videos with Neil: bit.ly/Sloane_Numberphile
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Riemann hypothesis solutions is complex irrational number. I have one theroy 🙏. Which platform I publish my theroy plz tell me. 🙏
What happens if you reverse the order of each numbers digits after passing N? Any primes there?
I am The Crazy Scientist and I left this message here for no reason whatsoever
Does this work in other bases?
Honestly, who wouldn't want endless boxes of chocolate?
He sounds like he gets out of bed in the morning and is absolutely thrilled he gets to do more math, every single morning
High on math
This comment is delightful. :)
He is a mathematic mathADDICT
You should see Cliff Stoll talking about Topology.
4:46
"Give me a prime"
"2^31 - 1"
Baller move. Brady should do that the next time Matt Parker asks for a number
I had a colleague say Graham probably knew something we wanted so I said he could call Graham's Number but it could take a while to get answered.
@@PMA65537
Graham’s number is definitely not a prime.
@@ragnkja you probably missed a joke. With 'call' the commenter meant 'making a phone call'.
A Parker Mersenne Prime? 2^67-1
@@ragnkja 2^G - 1 might be prime though!
Neil Sloane is always worth my time.
Whether it be odd, even or prime
He's worthy of prime time.
Neil Sloane is always prime time!
But is time worth Neil Sloane?
??
Seeing Neil Sloane enjoy his sequences (and talk about them) is always a pleasure. Please do more interviews with him in the future!
Please do it in some other bases, I’d love to see one in base 6
He's got major Jeff Goldblum energy.
We need MOAR....! Please?
Yes, please. I'm especially here for sequences and primes.
false.
The largest prime that I know the digits of is Belphegor's Prime:
1 0000000000000 666 0000000000000 1
Thirteen zeros before and after the number of the beast, 31 digits (13 reversed) in all.
Checkmate christians
That's so friggin cool
Of course, Numberphile has covered this number: the video "The Most Evil Number".
But are there an infinite number of primes of the form one, some number of zeros, 666, more zeros and a one? Or more than one even?
@@michaelsmith4904 the smallest prime after this one with 13 zeros is with 42 zeros (10000000000000000000000000000000000000000006660000000000000000000000000000000000000000001). also no zeros (16661) is also prime
He always seems like a child who has found something interesting to play with 😍
A Klein, interesting. You're a point of interest for Numberphile
Do you manufacture bottles by any chance?
I feel like a child who found something to play with and want to show other people my new thing!
@@avikbhattacharya6854 oh?
Yes, numbers are quite a fun thing to play with.
Great, now I can boast about knowing a 17000-digit prime by heart! Thanks
Be careful not to boast too loudly. Someone might ask you to write the number down. It could take a while.
Well, write it!
Read the Description. At the time of the video, it was only a probable prime.
@@RWBHere I really like how you future-proofed your comment.
@i liked how, at the time of reading, he had future proofed his comment.
@numberphile hey! I saw this and thought, "what about concatenating increasing values to the left" i.e. 1,21,321,4321,54321, etc.
Did a little bit of number crunching and the first one I found was at a starting value of 82.
They exist!
(I was able to speed up my search realizing that 2/3 of these are divisible by 3 and skipping testing those.)
Maybe look for the next one and make a video on it? Prime related videos are always a hit. :)
Anyway.... Loved this video! It inspired the little search I just did.
Well if these primes(assuming there will be more) don’t have a name yet, we could call them Falken primes
How far did you go? Judging by how fast the number grows there should be infinitely many (O(ln(ln(n))) below some starting value of n)
Ah, that's a nice prime.
Would that be the “least wanted prime”?
Wouldn't mind them being called Falken primes if there's no name yet.
I'm looking into other patterns that I'd be more keen to get something published for.
I didn't look past 82. Reason being I typed the number manually into an online primality test. I was more than happy finding 1. (I was willing to go up to 100)
I really need to code up something to do these things for me :)
Just an FYI, CCS is pretty much just a waste of money, and has never been demonstrated to be effective at reducing CO2 emissions.
4:39 "I'm not finished. I have another segment." I don't know why, but I really enjoyed that. He loves and can talk about numbers all day.
He better live to a hundred or I'm gonna cry
100 isn't a very interesting number - I say he should live to the age 1729
He should live for a whole number of years, to within a day.
Better to the age of N
@@blower5 No. Age 108. (because in base 6 it's 300). jan Misali has talked about why base 6 isn't arbitrary in 'a better way to count'
but 121 isn't a prime number. Here n=2
I would love to hear more from this gentleman, he can be a narrator for some great shows
Yes. He sounds a lot like David Attenborough.
Now, Stanley was- for the first time in his life- curious as to what the next prime could be.
He uses a lot of range.
??
"It's a story you can tell at parties." I'd love to go to a party where I get to hear Neil Sloane's stories!
??
Prime numbers and numberphile videos about them , never get old
I got curious and decided to try this - but with base-2 instead of base-10. And I think I found one!
01101110010111011110001001101010111100110111101111, which is 485398038695407, _is a prime_. And it contains the numbers from 0 (which might as well not be there) to 15.
I give you a virtual cookie
This comment needs more visibility!
Few others:
1 2 3 4 5 10 11 12 13 14 15(b6) is 4060073996291
1 2 3 4 5 6 10 11 12 13(b7) is 131870666077
12(b3) is 5, 12(b5) is 7, 12(b9) is 11, 12(b11) is 13, 123(b8) is 83
12345(b12) is 24677
(couldn't find anything in base 4)
Binary goes till 15 a multiple of five, 3 and 12 both go till 5. 12 and 5 together remind me alot of the golden ratio
This can actually be a big insight. Can't believe nobody bothered to look at other number systems so far!
@@CompilerHack Why does twelve remind you of the Golden Ratio? It is not a Fibonacci Number.
The professor has such a beautiful voice.
I'm intrigued by the sequences both so important and so hard to evaluate that they have the privilege to be included in the OEIS with only one entry. Tell us more about that please !
Someone else in the comments went and found all the one-term sequences on OEIS: A058445, A058446, A072288, A076337, A115453, A118329, A122036, A144134, A245206
How could something have more than one entry in the OEIS? What would that mean?
@@leif1075 They mean only one term in the sequence is known, and yet the sequence is included.
@@SSM24_ someone should make a submission made of the ids of the currently all OEIS sequences with one term
@@SSM24_ at least for A118329 the second term is known but too large to be included.
I would like to note that if the step between each number is 2 instead of 1 (so 135... instead of 123...) the first prime is 13, but the first interesting one is 135791113151719
Now that's fun
Wow
Someone should run this for other steps of n
So are 1357911131517191715131197531 and 19171513119753135791113151719
@@chrisg3030 Okay that's really cool
My new favorite hobby is reading all the comments on "the all 1's sequence" on the oeis.
Now I'd really like to know which sequences in the OEIS contain a single term
absolutely!
Came here to say this. You can't offhandedly mention extremely important single digit sequences and not give an example!
same!
A single term, not necessarily a single digit.
@@ragnkja _aCtUaLlY_
but yeah, you're right lol just edited the comment
I expect the most wanted prime number is the private key to some big bank's signing certificate, but this is maybe the coolest (to mathematicians)
It's gotta be one huge as key I tell you what
Private keys are composite.
banks do journaling once a day, so at best it'd be a big news item, but if the books don't square the transactions will not go through.
Huh, this is interesting... I actually got 2 "most wanted primes" in hexadecimal with n < 1000, the first is 123456789ABCD (n = 13) and the other is much larger (n = 211)
Which brings up an obvious question. What if you do it in base n+1?
@@jmodified Or base n - 1, so the last amount is base + 1 so that's relatively prime to the base, too.
@@jmodified No idea... I tested up to b=256 today and n
@@caiohomar1540 Does any base have a dedicated OEIS sequence?
@@iridium141 Don't think so, I couldn't find it at least...
Me: "Is this prime?"
Mathematicians: "hmm, not sure... BRING OUT THE GIMP!!!!!"
can't wait to whip out this story at a party
So happy to have Neil back
I love these videos with Neil Sloane. It's very soothing to hear him describe patterns.
I hope I'll have his energy at his age. Just a joy to watch.
And his voice! He is an awesome narrator, so engaged and excited.
I love your videos with Neil. Hands down my favorite guest on the channel!
Brady: Should we believe there are an infinite numbers of n's this will work for?
Neil: Yes, do the math.
Me: I don't think I will.
I don't think I can
@@GodwynDi Nobody can, yet.
@@GodwynDi If you have any sort of stem degree, then you probably know (or knew at one time) enough math to do it. I assume you would: look up "distribution of primes", find an approximate distribution of these numbers with a simple form - which looks easy, then determine if the sum of expected number of these primes computed from those results diverges - which could be difficult but is probably very easy. That is assuming of course that there is nothing "special" about these numbers in relation to primes, which seems very unlikely given the form of the numbers.
@@jmodified I probably could have when I graduated college, but that was near 20 years ago. And I don't use any complex math anymore. Still enjoy following the stuff though.
Well, the number of primes like this will be an extremely small subset of all integers. But, since there are an infinite number of integers, any subset with members that occur periodically would, by definition, also be infinite.
Neil is an absolute treasure, and it’s always pure joy to watch numberphiles when he is in an episode!
I can't bear the sound of that sharpie pen writing on that rough paper!
I was just binging all of the old Neil Sloane videos yesterday. So glad to see a new one!
I love the fact Neil has a ping pong table as a desk.
by the books in his shelf it´s nice to see Professor has also an interesting in Operating Systems (Unix) and computer programming (Shell)
His areas of interest are combinatorics and error-correction which explains his bookshelf.
I am still contemplating whether this is is an ingenious and pragmatic idea of just writing the contents of the stacked books on the side of the pages or the laziness of not getting a proper bookshelf and organizing the books where you can read the actual titles.
Not to mention R.
Thank you to Numberphile for showing me the beauty of mathematics. I was in high school learning algebra when I was also watching Parker et Al and understanding little, but appreciating the beauty seen by the presenters. Thanks Brady.
As comedian Chris Ramsay said: "I don't understand what's going on, but I'm enjoying it"
This is an absolute gem. Thank you.
I love Sloane's enthusiasm, it's infectious.
So is Cliff Stroll's
Great video.. more of Neil please.
Neil: I encourage everyone to continue the search and find that smallest value of n which is prime.
Me: Or prove such an n doesn't exist?
Its possible there an infinate many, just very rare. First counter example could be say n = Gogulplex (well heristically) and occur with probability 1/log_gogulplex n
We'd never find one of that were the case
Or prove that this puzzle is unsolvable (i.e. you can't prove it doesn't exist yet you can't find a smallest value that's prime)!
@@Anonymous-df8it You can't prove that this puzzle is unsolvable, because if there is such a prime, then once you know the example, it's trivial to prove that the puzzle is solvable, therefore, your "proof" that the puzzle is unsolvable proved that there is no such prime, which solves the puzzle and contradicts itself.
I guess Neil already knows that they exist, otherwise they would've mentioned that it hasn't been proved.
A petition to authorise 1 to be a prime number would solve this problem easily!
and break mathematics ;)
And then mathematicians would look for the 2nd smallest such number and we're stuck again.
This is why I love numberphile !
@3:40 I'd love to watch a video of these 1-term sequences!
is a 1 term sequence a sequence? or is it just a scalar
@@julianatlas5172 No one knows the second term.
I always want more Sloane content!
Nearly 4m subscribers, nice work. Hope you've got the special ready
Imagine being the 4 millionth subscriber lol
So why did Armand Borel want a prime of 20 or more digits? What was he planning to do with the answer? We never found this out.
(BTW, is Armand related to Emile Borel of the Heine-Borel Theorem?)
Fred
God I hope you have 100 Neil Sloane videos backlogged. This man is my math grandfather. What a treasure.
“Bring out the Gimp”
“But the Gimp’s sleeping”
“Well, you’ll just have go wake him up now won’t you?”
Your enthusiasm is SO contagious. 😁
I liked Neil's little moment of flailing, frustrated at being unable to find any primes.
Get me pictures of spiderman!
For the most wanted prime it's interesting that not only are n%2=0 definitely not prime. but because 10%3=1, also n%3=0 will definitely be divisible by 3 as the last one was and n-2+n-1 is divisible by3. But this carries over to n%3=2 as we know that the next number is divisible by 3 and that a multiple of 3 was added.
The same is true for n%11=0 and n%11=11-1. And the pattern holds for 111, 1111,...
Found out this wasn't true but the 3 one still is
This is gold. A true TH-cam treasure.
Neil is a joy to listen to
I really hope this video helps find the first prime like that.
me too!
me three!
Me 2^2
Me 2^2 + 1 (the 2nd weirdest prime number)
Time for a part 2 where Matt Parker writes some python code and almost finds one which we can call a Parker prime
😂
Remember rectangles are “Parker squares”.
I think I found a “Parker Prime” for you! If you write the numbers from 1 to 121 side by side and treat it as a long decimal number [which would likely too big to visualize in the observable universe] then that number's smallest prime factor is 278,240,783 [more than 80% of the American population].
Enjoy! :)
Neil is great and he is obsessed with prime numbers. Please show more of his videos.
The way he enounciates question is oddly soothing
Yeaah, Neil Sloane the Legend
Very base-10 heavy. The number 12345678910987654321 is indeed very memorable, and a nice piece of trivia at a party, but it seems like nothing particularly special because the fact that we write in base 10 is so arbitrary. I'd be curious to know if we wrote in base-12, for example, or base-n, whether either palindromic sequences or sequences that stop at n would be prime.
I feel the same way about 3301 and 1033 both being prime. Neat fact, but not very meaningful. People easily conflate the properties of the *representation* of a number, with the number itself (I think partially because people aren't taught much about other notations in school, especially other bases.).
This is related to recreational mathematics. You don't seek for beneficial in math at all, problem is problem. The number is in base 10 but It is not true that these problems are not important mathematically.There are serious problems in recreational math and the way to solve them sometimes lead to important areas.
As always, captivating, educational and entertaining. 😊👍
In base 3, not in OEIS, for most wanted primes (or pseudoprimes), you have:
n=2 12 5d
n=5 12101112 3929d
n=82 121011122021221001011021101111121201211222002012022102112122202212221000100110021010101110121020102110221100110111021110111111121120112111221200120112021210121112121220122112222000200120022010201120122020202120222100210121022110211121122120212121222200220122022210221122122220222122221000010001 112472248900628264609109603739848048285897664360560828256938844196881901607705808202739737387845865591848483833175481611716989149644798597217d
n=2546 12...a 17096 digits base3 number and in decimals: 43890161488751460546626702438613565060003336281644449680671137248224514688491538690975134899736580108040235144902850247124275888829167582111888208962431881069187554719673572324004400907342770369694358050895638847024397795010971505542791197193876977453786100380941871966222470323265996374093675914641362678086425952662353480926826428446406757377963278157666201416261682611228802339238477428776727632017540989988176195868147174041239187417604219543007022139243321058577590644959401984067191769030638388726906644028086903822159080075772603841931016576581760214138320362816303048679719547048722501702555633000390530689374516513680029408176364910292994228954902928969448658904462575577354071270800213912051201523507394365683111528565341198912876422694722144929638945967403245098708248404322530202727882676941072079153569222949337103192425966055684814431400044565451265813686761215405533643511789884617646328246743281720432328194095683194587785547508148773470772593738258801763760546794662073718516191928591072734651560403556002732524161730316142686268758260877916597511512003796528274036447792924499494864342440677602583759931789321793424298317396285449554955292586535836216021617023243141250119118512285946506249761293344929001780039983261592084263554914364441749840728216443011119067342706727925477712618231168978833958062652687921812610479346345264504765110030520074975442528118698445700483939782752609726084487308375967269514211813640018741875722580241863926703050300712545815352393120793488218413283618123570588307416854433864996494431522281803030485486558059502715089759852450544339517757804285967188699401114866728876776549756684736309852094725050865930800167370104933949388035243022389363378334680013923434066416861926258085816117742505281123833405809310964323493563189361527117878499659063347307304583402070651167772180308830540838123475351447507484992450520788644591125264607612093737901470944162813780897645548146351246209624486034557431548471720783210675389095371393790498285892636128668119451378240219077207134739752608785181867928263686385935215347914452582657142085011407738559212460959268691200770239157870204451164934062213679157927231503425082141878027811193566696609165091454874475721882598283385158300240762055794266047495929993818891307012591626969301205165344706934338840173319948265753741137524920248111206491006196652417307431031750699528179185458982562133803404685438296067156978853797336545647449025239991977998712697711265249729376743473555059777964135291443181725783056729552750299424308449273341836036581351481308211339703462171182093726530237263185892498101223377615500102312287248676936254608602229951158919989223765609446436479541916679149534365897182729707823017267283647397249900179384121021898332183399958586514174894501681280555416335242257069223054397177949751294731391574786389724838624019993383653689742946081760774109640742133417696582657530590909815179785635202106593346231901503857163231028136378224240545656107266082808509457244118432204364596748383545879295806117994595023772406415351247964030765052022307194245969684455877572521087343566249732952806269934334054705784570846540141977666647354223473972311288950609815860735838654476360384691259636542129738992987380417603981271846261521786588916834646357350934099126326728075067337322798596076189544486832952920264198426068039988068169743237688209371000314234636523906102826099011519696179003630302866491680295287097128551313032321293575929024306470092686558080746952275770835242360570930045228655204576322734523342849052530545974405199343183221590087859245300764078222862815288814207734442339460433012421856546439636266561975265503963066109237076379991393306132398275447039070424867309968987904427684423182702897381433098932224788146285245889721026254508998483143595198863424120430654450975773068603745141757057977594415814586925209888338894214617342925205156757352253040101332858321041516894759139574456898613064389079736487560664739435400868746702620299006861572577151088668428749705450014329385374165101664130899422691170661920102396003411157789363281244422411600247564749697988094095262218593242044279180823572957717109170056955699914724723828165141430769892345712501881108903022320421347100915124530872659403994296038150640065718827635199663190949646987849434145501509659086015263008665371714705277624397492086356504877074559834335005436733963222261337612984566084807359523673372914839433015018204943015330352599696510122346029749468281071434723897520884700709191513862252461006982884464210303147568253751881662056607466471401070638950718477367116659142364146394792699568224426051748009604323467662327479747880571417801026259794347390730849724019238094760895260627018391357674427100142529722180028599049119447849087294169503878161683194602136375471716666525377771670869918484418229582194639066294750852576218974124745820546263757377303828449999556216249892265725720667654811037842088818263095350793091393616240732601285395184407013946743728609257903977255811712828611203851591483970281282366272387476098249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Woah.
My favorite thing about all of the numbers where n is less than 10, they are all square numbers. The coolest part is that the square roots of all of them are all composed of numbers made of 1s
I assume you're talking about what Neil calls "memorable primes", such as 12345678910987654321 in the first part of the vid.
If we replace that '10' in the middle with 'A', a single digit equal to it by convention in number bases bigger than the usual decimal, then we do also get a square. In base eleven for example 123456789A987654321 is a square, as it is in base twelve and thirteen and so on. Even though the actual quantities that particular sequence of symbols represents differ from base to base, they're always squares as as long as we represent n with a single digit. The same applies in bases smaller than ten.
On the other hand, when we represent n as 10, then we don't always get even a memorable prime, let alone a square. In base eleven, again for example, where the number after the top single digit A is 10, the number 123456789A10A987654321 isn't a prime, besides not being a square. But in the hexadecimal base, in which the top single digit is F, 123456789ABCDEF10FEDCBA987654321 is a memorable prime.
@@chrisg3030 that's cool and flys over my head a bit, but I'm just taking base ten.
I'm always suspicious of messing around with functions that only work in base 10. It's not that this isn't a real problem that could be solved, it's just more than it feels like numerology instead of mathematics.
Yeah finding primes with a pattern so it's easy to remember how to write them out in base 10, not a real math problem. I guess numerology is playing with numbers like this?
This play does lean on serious math problems, like for each check to decide if a candidate number is a prime, it's helpful to use a fast method for finding a number's factors (this implementation quits when it finds any, or declares prime when the search ends in failure).
Conway's 'Look and Say sequence" is even more arbitrary, and yet it proved to lead to some interesting mathematical developments.
Every video of numberphile is so informative and enjoying, surely a boon for math lovers.
Loved how all his books and file folders are labelled and organised. 😍
Maybe it’s just his genuine enthusiasm for the subject he’s discussing, but Neil reminds me a lot of Richard Feynman in his mannerisms and speech.
N has a lot to answer for in mathematics. There is a huge weight on it's shoulders.
Yes the legend is back
I like the OEIS videos. I've toyed around with a summation/product style notation for concatenation in the past, and it would be fun to suss out equations for these numbers/sequences. I'm sure someone already has a better "big concatenation" notation, but some things are fun to put together yourself.
This climeworks actually sounds like setting up a timebomb for future generations.
Let's store it all underground, "fill" the "land" if you will. Nothing could possibly go wrong.
It honestly sounds like a big scam. I haven't looked into it, but:
How much CO2 is released from building these machines to extract it? (How long do they need to run to offset that? Factor in maintenance as well)
How much CO2 is released from running these machines? Even if they run on renewables, that amount of energy could be used somewhere else to replace fossil fuels.
Unless we have 100% electricity production from renewables, this doesn't make any sense in my opinion.
Storing it underground doesn't sound like a bad idea. I don't know what form they're storing it in, but it's probably basically just carbon.
I wonder if it is the "prime" accused in a crime?
Hello
Not nearly enough discussion is made about repunits (all 1's) as candidate primes. Worthy of more exploration!
His enthusiasm is infectious
GIMP is a graphics program. GIMPS is looking for primes.
2:40 Ten works! And 2,446! And beyond that we don't know... But we DO know there are an infinite number of them! And THAT's why I love Numberphile so much!
Well, to be fair, we don't KNOW that there are any more, we're just assuming that because it's a completely artificially constructed number so it's equivalent to picking at random (taking into account things like the numbers not being even etc) and we can calculate the probability of a number in a certain range being prime so we can calculate the average amount of primes in the first n numbers of the sequence and it diverges therefore one could say it's probably infinite
Why does this wrong comment get so many upvotes? We don't know, man!
@@christophermaurice2221 no it doesn’t. For N= 1 you get the number 1, which is not a prime.
@@gregoryfenn1462 1 is divisible only by itself and 1, checkmate
@@SlenderSmurf OK, but 1 is still not a prime number
he sounds like he's very well practiced at saying "sorry"
In the mid-1970s U was working on a project developing a small business computer system. My boss came up with a math library that would allow operation between any two numbers of arbitrary byte length. The CPU we were using was an 8-bit device.
As a test to see if the machine would work, sort of w wringing out, we programmed it to find the next Mersenne prime. There was no chance that we would, but it was a test we could evaluate to determine if the hardware and our system software were working correctly. It was actually fun and a bit challenging.
This is now the largest prime that i can keep in my head and write down :D
What does the most want problem look like in other bases?
Partial answer for base 2 n=15 (1111) Is prime (1101110010111011110001001101010111100110111101111) (485398038695407)
Spent some time working out a formula for the amount of digits of the number resulting from writing 1 up to n and back down to 1 written in base b.
d(2*n+1)-(2/(b-1))(b^d-1)
where d = floor(log_b(n))+1 or in other words the amount of digits of n when written in base b
after this i feel an immense need to go find that prime
I suggest another challenge: Try looking for this last kind of prime where the base=n.
Ah, I just suggested that above, using n + 1 though - otherwise you've gone one past the clean part.
Counting down instead of up (eg 1110987654321) might lead to more primes as every term will end with 1
I tested on Sage and it says that 828180...10987654321 is a 155-digit prime
best video on numberphile
This is amazing!
I always find this type of sequence (that relies on a specific numeric base) kind of "meh". _Relevant_ stuff in maths is about _values_ and their properties, not about the characters you use to write them with. If the "property" you're looking for only works in base 10 but disappears in base 11 or base 8 or whatever, it's just a curiosity. It might tell you something interesting about that base (and that is especially true for base 2, which overlaps with logic / boolean algebra), but not really about the number sequence itself.
I definitely agree. But having said that, it's pretty cool to know by heart the decimal digits of a prime number that is thousands of digits long...
How on earth do they manage to prove that the 17,350-digit number is prime?
Lots of computers screaming in pain.
They tested for a number with 646 million digits (2^2147483647 - 1) it turned out to be composite
Niel Sloane lifts my spirits.
with Neil Sloane!
An interesting question would be the following: when we are testing for primes, just “counting upwards”, since they have now made it to 1000000, and he said it seems statistically likely that a prime should have shown up and it hasn’t, I would think it would be an interesting idea to try and figure out WHY you can’t hit a prime counting upwards in this fashion and maybe prove it true or false. What do you guys think?
My thought exactly are we sure that there actually exist a n such that the number becomes prime.
You can find primes like this in other bases though, so the chance that one doesn't exist in base 10 would be startling! If it is the case that none exists, and it can be proved that none exists, it would be interesting to know in which bases these sort of primes can or cannot be found.
@@LunizIsGlacey Someone gave it a shot in various bases and bases 4, 13, 18, and 19 also don't have small primes of this form.
@@coopergates9680 May I ask where you got this info?
@@iridium141 Did it work when I tried to tag you in the thread where someone offered that info?
Math, an endless playground.
I love that Brady always films Neil Sloane in a Whataburger.
3:02 - Seems guaranteed to get you invited back.
I wonder if the 1 .. 10 .. 1 prime works for every base you write the number in (like stopping when you reach the base). It seems to work for base 2 and 3
It worked for 4 but failed on 5, from my test. I might have messed up and it was a quick n dirty test and some of my tools might be bad, but thats what I got at least
I tried 16 too and it works
@@sock7896 Is 5 the *only* counterexample?
We got James Grime after a long time, now Neil Sloane...just missing takashi tokeida now
soon
@@numberphile ヽ(=´▽`=)ﾉ
Cool that he gets to work in a Whataburger themed office.
I love the way he says, “Sorry!”
Based on my careful observations of this channel, I’ve come to realize every competent mathematician on earth has butcher paper and a sharpie.
They bring it with them but yea u are not a math guy if u dont have papers and a sharpie flying around on your desk
I'm curious about other bases. Is it just a coincidence that the first one works for n=10 in base 10?
It works for base 2.
@@nverwer 1101(2)=13(10) is prime, yes. It also works in base 3: 121021(3)=439(10) is prime; and in base 4 as well: 12310321(4)=27961(10) is prime, too. 5 is the first one where it's not prime, because 1234104321(5)=3034961(10) is divisible by 137.
This is actually in the OEIS, as sequences A260852 and A260343. So, the bases where this works are: 2, 3, 4, 6, 9, 10, 16, 40, 104, and possibly 8840 (but the last of these is only a probable prime, with 69770 decimal digits).
@@renerpho Huh, no one checked it yet? 70k digits should be barely solvable by supercomputers I think
@@viliml2763 There are a lot of 70k digit numbers. It seems like indeed no one got around to check this one yet.
This is great. Problems that I can actually both understand and appreciate.