back to article Frenchman calculates 13th root of 200-digit number

Frenchman Alexis Lemaire yesterday broke his own record for calculating the 13th root of a randomly-generated 200-digit number, pulling off the impressive mental feat in just 70.2 seconds. The 27-year-old "mathlete", who's doing an artificial intelligence PhD at the University of Reims, indulged in a "great deal of brow- …


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  1. Robert Grant Silver badge

    I like his logic

    If I think like a computer, then that thought process can be recreated in a computer - we can make computers that think like computers!

  2. supermeerkat

    Herbert B de Grote!

    <nelson>Ha ha!</nelson>

  3. Anonymous Coward
    Thumb Down

    How very French

    How very French of him... in the sense of French meaning pointless... hands up who has EVER needed the 13th root of any number, let alone a 200 digit one... keep those hands up if you've needed said result without being able to resort to some form of computer. Now keep those hands up if you've needed it within around 70 seconds.... what? no hands?

    Wasted life me thinks!

    As for "If I run a computer programme all the time in my head, it should be possible to download it to a computer programme and that leads to mind-uploading. This would mean the computer would have all the same skills as me. I think it is possible."

    - I think we've uncovered amanfrommars' true identity?? Or is it just another sad Frenchman with a loose grip of English

  4. Richard Tobin

    Very slightly easier than it looks...

    Because it must have ended with 13 zeros. Also, the 13th root of any 200-digit number starts with "2".

  5. Gilleain Torrance

    You what?

    Seems either a trivial problem (emulate a computer program on a computer) or a hard, but pointless one (emulate a brain emulating a computer, on a computer).

    Either way, as useful as finding roots in your head; that's why we invented computers, to do those kinds of dull calculations, you tool!

  6. Chris Miller

    Unlike a computer

    This is certainly a very considerable mental feat, but I very much doubt the approach he uses bears much resemblance to that of a computer. If I wanted to do this (in my case, this would require the use of pencil and paper :), I'd memorise the 13th roots of 10^199 and 10^200 (~2.03E15 and 2.43E15) and then use something like Newton's method to triangulate to the correct answer. This would require the ability to raise 13th powers of 16-digit numbers in your head - no mean achievement in itself!

  7. Neil


    This person can mentally do what a computer does, only presumably a lot slower? Useful...

    In much the same way, I can walk somewhere but it's much quicker to go by car.

  8. Senor Beavis

    @ Chris Miller

    Is that a bit like estimating the number of sheep in a field by counting the legs and dividing by four?

  9. Anonymous Coward

    If I was thinking like a computer...

    I would have realised halfway through crush hour that the human race needs to be systematically cleansed from the earth.

  10. Spleen


    I did a search because I wanted to know what the guy looked like (surprisingly normal apart from the regulation stupid facial hair). I found a BBC article ( in which Lemaire was breaking his own record back in July, at 77.99 seconds. I'm too lazy to research when he first started trying but getting in the newspapers for breaking his own record seems to be a regular occurence. Perhaps now he's in the Guiness Book Of Records (coming to a Christmas tree near you courtesy of a relative who doesn't know you from Adam) he'll have a go at something different.

    While reading that article this gem caught my eye:

    "Researchers have tried to link problems with the brain either through trauma or malformation to extraordinary mental abilities - one of the theories being that damage to one area prompts compensation in another. Brain scientist Dr Allan Snyder has suggested that everyone may possess such abilities but be unable to access them. "

    I suppose this is in the same sense that I am roughly the same height as Amir Khan and also possess two legs, two arms and have all the same bones and muscles in the same places. Therefore I possess the ability to box like Amir Khan, I'm just unable to access it. Who pays scientists to trot out this meaningless nonsense?

  11. Tony Barnes
    Thumb Down

    @ everyone bar Chris Miller so far (and maybe supermeerkat...)

    Seriously, are you putting this guy down for wanting to be able to mentally perform an outwardly nigh on impossible task???

    It's backward thinking muppets like yourself who set back intellectual innovation. Give yourself a clap, and go try and work out you 5 times tables...

  12. Rich Silver badge


    "Is that a bit like estimating the number of sheep in a field by counting the legs and dividing by four?"

    What if some of your sheep only have three legs? Buggers up your calculation then. And if your sheep still have tails then they could be mistaken for legs! And what if they are climbing on top of each other shagging? Your result is going to be WAY out!

    On balance, I think your approach has a number of flaws that need addressing.

  13. Andy


    I think you're missing the point here, but in any case your logic could be applied to denigrate any pinnacle of performance. Who really cares how fast a man can run 100m in when we have jet planes? Who really cares how high a woman can jump now that we have space flight? You're just imposing your idea that life is all about having a pint at the pub with a packet of crisps (or whatever it is you do). Of course anybody who is different than you is wasting their lives and shouldn't be encouraged to continue breathing.

    The fact that he's doing a PhD thesis in AI and sounds like a complete nutcase to me ("running a computer program in my head" denies any conception of emotion or spirituality or otherwise 'humanness') is interesting and possibly exciting. He could be the creator of our new mechanical overlords and I think we should keep a video on him at all times so that we can catch a glimpse of the terminator who comes back to kill him.

  14. Anonymous Coward
    Anonymous Coward


    But I want to know who programmed the “flock of seagulls following the trawler”

  15. Anonymous Coward

    RE: Unlike a computer

    Erm, how do you reckon computers calculate roots then? From my recollections of maths and computer science at university, there isn't a "formula" or calculation to do this without some form of recursion. Whether it's through Newton's method, or by doing some logarithmic calculations (again, generally involving recursion to approximate it)

  16. Anonymous Coward
    Anonymous Coward


    "Because it must have ended with 13 zeros."

    What?? It wouldn't have to...

  17. Anonymous Coward


    "Very slightly easier than it looks...

    Because it must have ended with 13 zeros. Also, the 13th root of any 200-digit number starts with "2"."

    Not quite right Richard. Yes they will all start with a "2". There are

    393544396177594 exact 13th roots of 200-digit numbers so he can't have

    memorized them all. They don't all end in 13 zeroes, in fact only 10% do (all the

    ones where the root ends in a zero). For example the 13th root of:





    is: 2296222986023825

    Not many zeroes at all.

  18. Jerry Adamson
    Thumb Up

    Bravo !

    Pascal, Descartes, and Poincare would be proud.

  19. Clovis


    Hmm, a number with 200 random digits which ends in thirteen zeros? That's likely. They must have been using Excel's rubbish random number generator?

    Or perhaps they could generate next week's lottery numbers too?

  20. Tony Barnes
    Thumb Up

    @ anonymous coward

    Shit, that's just underlined how bloody hard this feat is. It's taken me about 40 seconds to read every digit of that number out, let alone piss about with it in my head...

  21. Anonymous Coward
    Paris Hilton


    This 13th root nonsense is a stalking horse. What's really going on here is a French plot to destroy civilisation by teaching computers how to do the Gallic Shrug and go on strike. Be afraid.

  22. Phil Rigby
    Paris Hilton


    He did say "estimate". Not an exact count.

    Plus I don't see the point of what he did. Yeah it's clever, but then so is installing Vista on a Mac. Clever to do, looks good, but no real point to it.

    I read somewhere a while ago that (apparently) the average person only uses 1/3 of their total brain. Maybe this guy has tapped into the 2/3 of his. Or something. I guess it's like when you look at the motherboard of your PC - you can see spaces and holes for components that aren't there... and you wonder what you'd get if you put the components in... umm ok, I'll get my coat.

    Now for the icon of someone who hasn't even tapped into that 1/3 of her brain.

  23. Alan Parsons


    Or at least a [SIC] if he's being quoted?

  24. M. Poolman

    @RE: Unlike a computer

    nth root of x = 10^(log(x)/n)

    Most likely done using 2 as the base of the log though,

    and a Taylor expansion to calculate the log (iterative, not recursive).

  25. Ross Fleming

    @Richard Tobin

    I'm assuming that they were looking at the nearest whole number to the 13th root. Most 200-digit numbers won't have a whole root, and he'd end up calculating an irrational number and going on for some time. So the correct answer is probably along the lines of 2407899893032210 point something or other.

  26. yeah, right.


    He should go the USA and apply for a patent on his method. After all, he's just programming his brain, so it's software, so it's probably patentable in the USA.

    Alternatively, it would be nice if he developed a method for teaching his mental mechanism to others, rather than keeping it secret. These kind of things might be useful in helping people improve their minds. Who knows where such mental gymnastics could lead?

  27. Sam


    Can he "fart in your general direction"?

  28. fluffy

    @AC re @Tobin:

    Tobin wasn't saying that ALL integral 13th powers of numbers would end in 13 0s, just that this particular one did, as the root (helpfully provided in the article) ended in a 0.

  29. Anonymous Coward
    Anonymous Coward

    Seems a little selfish keeping the method to himself

    But then again, these kind of mathematical geniuses tend to have borderline personality disorders/severe aspergers/autistic, I guess it's the kind of behaviour we should expect.

  30. Anonymous Coward

    We forget

    Just because we're used to computers running MS software, we rule out all possibility of them having emotions and spirituality....

  31. Antony Riley
    Thumb Up

    Method is easy.

    Basically you just take this algorithm and customise it for 13th roots instead of square roots.

    It would require memorising some 13th powers, but the maths in your head and the number of things you need to keep track of aren't that difficult if you train yourself to do it.

  32. J

    Ah, the old myth...

    "I read somewhere a while ago that (apparently) the average person only uses 1/3 of their total brain."

    Well, while it might seem like some people do indeed possess only 1/3 of their head stuff sometimes, every normal person uses 100% of their brains.

    I doubt this guy can teach anybody how to do this. He is probably like the "real Rainman" Kim Peek, or that Brit (Daniel something?), and see forms and colors and the number just pops out or something like that. Something probably so strangely alien to us that we can't even understand, let alone consciously reproduce.

  33. jose

    How does he do it

    The method is simple.

    Take the inverse log of log(x)/13

    provides the 13th root of any number.

    Try it!

    To what level of accuracy is this guy performing this task?

    How many digits? Is it a whole number? No fractions?

    Since I don't have a 200 random number generator, I can't test for form of the solutions.

    Consider memorizing the log's for numbers 1 through 10 to 10 decimal places.

    How accurate would your results be?

    I was amazed by a slide rule and could not understand how it worked until Algebra 2 and I learned about logarithms. Afterwards, I used to do "amazing" multiplications and square root calculations in my head by memorizing the log's of 1-10 and the sin of 10 -90 degrees by 10. I easily had 3 digit accuracy which is sufficient for most problems. You just have to keep up with the zeroes.

  34. Chris G

    Bloody hell!

    This guy is one smart cookie! I just hope that he is not the one to develop the first true artificial intelligence that becomes the norm for all those that follow. Can you imagine the world's AI s with an attitude like a french customs official with a Gauloise in the corner of it's mouth combined with onion breath and a penchant for being difficult simply because it can?

  35. Anonymous Coward


    1/√2 = 1.41421356237309504880168872420969807856967187537694807317667973799 and that's just off the top of my head

  36. Anonymous Coward


    "He could be the creator of our new mechanical overlords and I think we should keep a video on him at all times so that we can catch a glimpse of the terminator who comes back to kill him."

    ....the terminator _THAT_ comes back...

    As to our man, please wake me out of my drunken stupor when someone has invented the device that does a meaningful non-destructive readout of the state of a nervous system of something larger than a roach (and it must be able to subsequent emulate it by either an program "equivalent enough" or by full simulation)


  37. Richard Scratcher


    What a waste! Instead of mucking about calculating 13th roots, his self-boggling mind should be applied to more lofty tasks, such as calculating the ultimate life...the know...everything.

  38. Nick

    hmmm, that's a good log

    For the method I'm going with the taking the log, dividing by thirteen and then raising back to the solution.

    How he got the logarithm is another matter. Did he memorize log tables, iterate in his head or do something else?

    Thanks El Reg for getting me to brush off my arbitrary precision coding. Raising 2407899893032210 to the 13th power gives:


  39. Anonymous Coward

    In my humble opinion...

    dude just needs to get laid

  40. Kanhef


    That works, but taking the log of a 200-digit number, followed by the inverse log of ~16, is still a non-trivial task. You'd necessarily need 16 digits of precision, better to have 18 or so to avoid rounding errors (the number was probably chosen to have an integer answer, but the log is still floating-point).

    For everyone who believes they use only 1/3 (11% / 10% / etc) of their brain, please indicate the unused portion so that we may remove it for you. Since you weren't doing anything with it, I'm sure you won't notice the loss.

  41. JeffyPooh

    Here's how 'e did it...

    It's bleedin' obvious. 'e 'ad d answer written on 'is cuff, natch.

  42. Kurt Faasse

    shades of delaney

    Is this a taste of "Babel-17"? Human brain as computer? Hardware in the wetware? The future is coming, ffolkes, and nobody, not nobody not nowhere, is going to be ready for it. That's what makes it fun.

  43. joe

    That's Freaking Amazing but...

    Can he understand amanfrommars? How's his social skills? Can he pick up chicks?

    With an outfit like this:

    You know he's a lady killer :)

  44. Chris Miller

    Thirteen zeros

    I'm sure that he must have been given a 200-digit (pseudo-)random number that didn't end in 13 zeros. The answer he produced was rounded to the nearest integer and happened to end in zero - a 1 in 10 chance.

    PS not even amanfrommars can understand amanfrommars!

  45. Adam Collett

    Life, Universe....Everything?

    Simple, the answer is 42...

  46. Liam Johnson


    Nope, sorry, you are wrong from the first digit onwards

    1/√2 = 0,70710...

  47. James Condron


    remember that old april-fool joke about malicious code being used when viewing web pages in your brain?

  48. xjy

    mental arithmetic - speed maths

    A simple and fun way of astounding people if you like cribbage is set out in the Trachtenberg approach to "speed math" - see for example

    or buy the book at Amazon for ten dollars:

    Language freaks and interpreters can astound people in the same way. Like conjurers. Or stenographers, or superfast typists, or piano prodigies. People are amazing. We've hardly scratched the surface of what we're capable of internalizing and manipulating in terms of patterns of numbers, relationships, movements etc.

    Basically it's in all of us. So stop emptying yourself of skill and potential and realize you're full of more than shit. Merry Xmas.

  49. Neil Gerstenberg

    Great memory feat

    I'd be really impressed if he demonstrated multiplication of two 13-digit numbers picked at random by a computer... Shakuntala Devi did that in 28 seconds.

    It looks like Mr Lemaire, shy as he is, would like to be the only authority of the only "Official" 13th root Universe Records list, with himself as only member. He also claims Guiness Records are "really stupid" on his website, and gives a mysterious link to "Apocalypse" revelation...

    I think all these years memorizing huge tables of numbers may have driven the poor man mad. Check out his website and see for yourself:

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