I'm sorrythat I didn't evennotice I I learnedfromsomebodyelse's postingthatoneofthenumbersofprime, so I hadn't noticedthatwefoundthreeinjuresWho's Cube?

Some 2 33 Thisnumberwasimmortalizedin a paperbyBjornPutin.

Now, onthefaceofit, thisis a threedimensionalproblem.

Okay, we'vegotthreevariablestosolvefor X, y and Z.

Andifyoujustwentthroughallpossibilitiesuptobethatsomewhereontheorderofbecubednumberstocheck, I saidyoucanimagine B is a 1,000,000.

Toputthingsinperspective, yoursmartphonecoulddo a 1,000,000 thingsintheblinkofaneye.

A 1,000,000 calculationslikethis.

Okay, butif I say a 1,000,000 cubedallright, that's intherealmofpossiblebutveryexpensive, um, todoonmoderncomputers.

Sothisisactuallyverywasteful.

Soit's nothardtoseethatinthesearchrange.

There's loadsofplaceswherethere's nopointinlookingOkay, Soif I imaginethat X, Y and Z areold, positiveandlarge, andofcourse, there's nowaythat, uh, someoftheircubesisgonnabe a smallnumber.

Itturnsoutthat l Keysalgorithmismostefficientwhenyou'relookingfor a solutionforlotsofnumbers, um, a CZwewerefor a whileButyoucanseewe'regettingdownto a prettyshortlistatthispoint.

So I startedtothink, Well, maybethereareotherapproachesthatwecouldlookat.

Myapproachusesmorealgebra.

Sowhat I'lldois I'lltakethisequationandthenwe'llmove Z cubedovertotheotherside.

Okay, Sothatgivesus X cubed, plus y cubedequals 33 minus Z cubed.

Thisisnow X plus Y X squaredminus x y.

That's whysquaredequals 33.

MinussaidCute.

Okay, now, whyhave I donethat?

Well, um, wehavethisfactorthatthatweknowisthere.

Okay, I'm gonnagiveus a name.

I callit d sayfordivisor.

Allright, thatonemorestep.

And I promisewe'regettingtotheendofelderbreath.

Let's dividebothsidesby D.

Okay, so I'm gonnahaveontheleftsidejustexpertminus X y plus y squaredrightside 33 minus Z cubedover D.

Nowitprobablylookslike I'vemadethings a lotmorecomplicated, right.

Westartedwiththreevariables.

Nowwebefore, but I wantyoutoimaginefor a momentthatweknowthevaluesof Z andof D.

OrmaybewehavesomeguestsforWell, thatmeansthateverythingintherighthandsideissomething I knowor I cancompute.

Onthelefthandside, I have a quadraticequationwithtwounknowns.

I'vegotonehere, butthere's anotheronethat I usedimplicitlybutdidn't writedown.

Andthat's thisone.

So X plus Y isequalto D.

Allright, sonow I'vegot +22 equationstounknowns.

Weknowhowtosolvethis.

Ormoretothepoint, if I guessvaluesfor Z and D.

I cantellprettyeasilywhethertherearecorrespondingintegervaluesof X and y okay, andthisistheidea.

Wejustgothroughallpossiblevaluesfrizzyand D, andseeifthere's anycorresponding X and y.

Andnowthatagainsoundslikeitshouldbesomethinglike B squared, right, becausethere's twovariables, butthekeyis, once I'vepicked a valuefor Z, thevaluesfor D actuallyquiterestrictedbecausetheyhavetobedeviseer's ofthisnumber 33 month.

Ishecute?

Andtherearen't manyofthose.

Soonceyou'veworkedout, see, youcanworkoutallthepossiblevaluesfor D prettyeasily, andthenjusttryallofthem.

I'velostover a fewthingshere, Soinactualpractice, youdoittheotherwayaround.

Yougothroughvaluesof D, andthenyouworkout Z fromthere.

Butyeah, that's theidea.

In a nutshell.

I uselotsofcomputers, actually, a fewseparateclusterson, andthecomputationthatfoundthesolutionwasthebigcomputerattheUniversityofBristolBlueCrystalphasethree.

Thishappenedwayfasterthan I wasexpecting.

So I startedthis.

I thought I wasinfor, youknow, sixmonthsofcomputation.

Myinitialfearwasthatnothingwouldturnupandthen I'd havetojustifywhy I wasusingsomanyCPUcycles.

Yeah.

Soonas I startedusingcomputerwithin a fewdays, itfoundthesolution.