The Most Wanted Prime Number - Numberphile 

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He sounds like he gets out of bed in the morning and is absolutely thrilled he gets to do more math, every single morning

"Give me a prime" "2^31 - 1" Baller move. Brady should do that the next time Matt Parker asks for a number

Neil Sloane is always worth my time.

Seeing Neil Sloane enjoy his sequences (and talk about them) is always a pleasure. Please do more interviews with him in the future!

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.

He always seems like a child who has found something interesting to play with 😍

Great, now I can boast about knowing a 17000-digit prime by heart! Thanks

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.

Just an FYI, CCS is pretty much just a waste of money, and has never been demonstrated to be effective at reducing CO2 emissions.

I would love to hear more from this gentleman, he can be a narrator for some great shows

Prime numbers and numberphile videos about them , never get old

He better live to a hundred or I'm gonna cry

"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!

@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.

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.

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 !

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

I love these videos with Neil Sloane. It's very soothing to hear him describe patterns.

Now I'd really like to know which sequences in the OEIS contain a single term

So happy to have Neil back

My new favorite hobby is reading all the comments on "the all 1's sequence" on the oeis.

I was just binging all of the old Neil Sloane videos yesterday. So glad to see a new one!

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)

can't wait to whip out this story at a party

Neil is an absolute treasure, and it’s always pure joy to watch numberphiles when he is in an episode!

I love your videos with Neil. Hands down my favorite guest on the channel!

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.

This is why I love numberphile !

I love Sloane's enthusiasm, it's infectious.

This is an absolute gem. Thank you.

I can't bear the sound of that sharpie pen writing on that rough paper!

I hope I'll have his energy at his age. Just a joy to watch.

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)

Loved how all his books and file folders are labelled and organised. 😍

This is gold. A true RU-vid treasure.

Great video.. more of Neil please.

Nearly 4m subscribers, nice work. Hope you've got the special ready

I always want more Sloane content!

God I hope you have 100 Neil Sloane videos backlogged. This man is my math grandfather. What a treasure.

I love the fact Neil has a ping pong table as a desk.

I liked Neil's little moment of flailing, frustrated at being unable to find any primes.

The way he enounciates question is oddly soothing

I don't normally get into theoretical maths but I love this guy's energy.

Yeaah, Neil Sloane the Legend

by the books in his shelf it´s nice to see Professor has also an interesting in Operating Systems (Unix) and computer programming (Shell)

Neil is great and he is obsessed with prime numbers. Please show more of his videos.

Neil is a joy to listen to

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.

A petition to authorise 1 to be a prime number would solve this problem easily!

Your enthusiasm is SO contagious. 😁

Every video of numberphile is so informative and enjoying, surely a boon for math lovers.

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.

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.

As always, captivating, educational and entertaining. 😊👍

Yes the legend is back

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?

This is now the largest prime that i can keep in my head and write down :D

Me: "Is this prime?" Mathematicians: "hmm, not sure... BRING OUT THE GIMP!!!!!"

His enthusiasm is infectious

I really hope this video helps find the first prime like that.

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.

Not nearly enough discussion is made about repunits (all 1's) as candidate primes. Worthy of more exploration!

This is great. Problems that I can actually both understand and appreciate.

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

Time for a part 2 where Matt Parker writes some python code and almost finds one which we can call a Parker prime

What a delightful man. Would love to sit and listen to him ramble about mathematics over tea

Niel Sloane lifts my spirits.

@3:40 I'd love to watch a video of these 1-term sequences!

N has a lot to answer for in mathematics. There is a huge weight on it's shoulders.

after this i feel an immense need to go find that prime

I love the way he says, “Sorry!”

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

I suggest another challenge: Try looking for this last kind of prime where the base=n.

This man is so wholesome, I wish he could teach at my university.

I realized at the end that I had been smiling throughout the video

I wonder if it is the "prime" accused in a crime?

This climeworks actually sounds like setting up a timebomb for future generations.

One of my favourite maths geeks!

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.

GIMP is a graphics program. GIMPS is looking for primes.

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.

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.

best video on numberphile

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!

How on earth do they manage to prove that the 17,350-digit number is prime?

This is amazing!

with Neil Sloane!

Counting down instead of up (eg 1110987654321) might lead to more primes as every term will end with 1

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?

There's something so trollish about that "sorry!" and I love it.

Outrageous. Absolutely preposterous.

1111111111111111111 is a prime in base-2, base-10, base-11 and base-12. It is also the seventh Mersenne prime (2^19-1 or 524,287) written in binary.

Ι wish i had the inner peace to just enjoy math videos like these without thinking of my problems

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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“Bring out the Gimp” “But the Gimp’s sleeping” “Well, you’ll just have go wake him up now won’t you?”

We got James Grime after a long time, now Neil Sloane...just missing takashi tokeida now

Math, an endless playground.

I love that Brady always films Neil Sloane in a Whataburger.