back to article 45th Mersenne prime discovered (possibly)

Distributed computing hasn't folded us a cure for cancer yet, but these projects in which PC users donate their spare processing power to solve scientific problems have unquestionably made major strides in uncovering ridiculously large prime numbers. Fans of bountiful digits may soon be rocked by the potential discovery of the …


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  1. Peyton
    Paris Hilton

    I followed the link, but still don't know

    While I can understand that a 10 million digit long prime number is a somewhat unique item, can someone elaborate on why it is worth $100,000? (well, aside from just the EFF putting that bounty on it) I know primes are used in encryption, but 10 million digits seems, to me, too long to be useful...

  2. Del Merritt

    I think 9 < 10 is still true

    "the 44th Mersenne prime is 232,582,657-1, which works out to be 9,808,358 decimal digits long.... The 45th Mersenne prime may qualify for a $100,000 prize ... to anyone who discovers a prime number with at least 10 million digits."

    Um, last time I looked, 9 is less than 10, and by standard mathematical rules, 9 *million* (and change) is still less than 10 *million*.

    So just how could they have a valid claim on the prize? No - the assertion that 0.99999... == 1 doesn't wash in this instance.

  3. Martin Penny


    Erm, sorry to be utterly anal and pedantic, but I'm sure that 15 and 63 aren't prime, being 3*5 and 7*9 (or 7*3*3) repectively?

    Mine's the one with the pockect calculator in (guess where?) the pocket.


  4. soaklord

    @ Del Merrit I think 45>44

    The 44th Mersenne prime was 9808358. They think they have found the 45th. And *that* number could very well be 10M digits.

  5. Ru

    Re: I think 9 < 10 is still true

    So, by your cunning reasoning, you demonstrate that the 44th Mersenne prime, which has less than 10 million digits, doesn't qualify for the prize. Well done. The prizegivers obviously thought so to, otherwise they'd have awarded the prize already.

    The 45th prime is going to be bigger than the 44th. The 44th was 650,000 digits longer than the 43rd. This does vaguely suggest that the 45th will have over 10 million digits.

    Do pay attention.

  6. Martin Penny


    Oopsie - should have read the article a bit more closely first; the it clearly differentiates between "Mersene numbers" and "Mersene primes".

    Shuffles away in embarrasement...


  7. Anonymous Coward

    @Del Merritt

    The assertion seems to be that, as the 44th Mersenne prime is just under 10 million digits long, the 45th Mersenne prime may well be over 10 million digits.

  8. Damn Yank

    "He estimates completion on September 12 and September 16"

    Shouldn't that be September 11 and September 15??

    I'll go now...

  9. Tim Bergel


    Doubt I'm the first one to say this but ...

    It was the 44th Mersenne prime that is 9,808,358 digits long, and the 45th that might be more than 10 million. That's 45, not 44.

  10. Carl

    you are wrong

    because 44 is not 45

  11. adnim

    What would be impressive

    would be someone discovering this number using mental arithmetic.

    Perhaps Paris should be tasked with finding the 46th.

  12. Solomon Grundy


    That's what it is: pants. This isn't a big accomplishment - anyone with enough CPU's could have done it. The reason that GIMPS did it is because they are a bunch of beggars whose project couldn't get enough funding to solder together a bunch of PS3's and come up with the number on their own. Pants.

  13. Sleeping Dragon
    Paris Hilton

    Nice to see...

    ...such clever minds take time out from other pursuits like finding cures for cancer, sustainable food production, and how to increase my bandwidth so that I can download porn faster than mankind can create porn sites to host it all on?

    OK, joking aside, really, what's the point?

    Paris - porn, she knows what I'm talking about.

  14. John H Woods Silver badge

    @@Del Merrit,

    Del Merrit is clearly joking ... he even gives you the hint by asserting that zero point nine recurring is not equal to one. Only jokers and fuckwits say that.

  15. Anonymous Coward
    Anonymous Coward

    Guys - you need to go to the pub


  16. Steve VanSlyck

    Send the money now!

    I have calculated the largest prime, also the largest Mersenne prime: infinity. You may send me my check now.

  17. Anonymous Coward
    Anonymous Coward

    More pedantry please

    What may have been found is the 45th *known* Mersenne prime. Saying just "the 45th Mersenne prime" means the 45th smallest, and it's at least somewhat plausible that there are Mersenne primes that, through accident or malice, GIMPS missed.

    So for example, M(32582657) is the 44th Mersenne prime to be discovered, and the 44th smallest of the known Mersenne primes, but that doesn't necessarily mean it is, as the Reg claims, the 44th Mersenne prime. M(127) was proved to be prime before M(61) was, but that doesn't make M(127) the 9th Mersenne prime and M(61) the 10th.

    It's as certain that those found BY gimps really are prime, btw, as we can be of any computer proof, since the verification process doesn't rely on thousands of people on the internet to all tell the truth. So these pair aren't any *less* than the 44th and (assuming verified) 45th Mersenne primes. But they might be more.

  18. Anonymous Coward

    M45 may be less than M44

    The process of searching for the possible new Mersenne prime is non-sequential. There's always a chance that the 45th *found* number would be in fact less than the previous one(s). That has only happened before with very "small" Mersenne numbers (centuries ago), and not yet in modern times. You can check the Wikipedia -- see numbers in the first dozen.

  19. Anonymous Coward
    Anonymous Coward

    Ohh if you real want to spice up the conversation with a mathematician

    Just claim that 9.9999 recurring is not equal to 10, because the 9 is not 10, so there will be a very very very small difference. Then ask them if they also hold that 1.11111111 recurring in base 2 is equivalent to 10.

    Oh, watch the mathematical sparks fly :)

  20. Anonymous Coward

    Confirmation Date

    Mersenne prime + Large Hadron Collider = 10th September is end of the world.

  21. Andre Carneiro

    And now, for something completely.... errr, pointless?

    Fine, OK, so maybe not pointless.

    But as stated earlier, I would be REALLY curious to know why millions of computer-hours were invested in THIS instead of something more obviously beneficial to mankind...

  22. Anonymous Coward

    Re: Send the money now!

    I think you'll find that infinity is divisible by an infinite number of numbers.

  23. Timbo
    Paris Hilton

    @Steve VanSlyck

    >> I have calculated the largest prime, also the largest Mersenne prime: infinity...

    I counter that, coz I've just come up with a bigger number, which is your number (infinity) plus 2......

    So, you can counter sign the cheque and send it on to me....

    PH.....coz she's worth every penny......

  24. Anonymous Coward

    That's perfect of course

    As Euclid proved llong ago, if M(n) is a Mersenne prime, then the larget number P(n) given by (4^n - 2^n)/2 is a perfect number. Thus we have:

    M(2) = 3, P(2) = (16 - 4) / 2 = 6

    M(3) = 7, P(3) = (64 - 8) / 2 = 28

    M(5) = 31, P(5) = (1024 - 32) / 2 = 496

    M(7) = 127, P(7) = (16384 - 128) / 2 = 8128

    These numbers are described as perfect because in each case the sum of factors is equal to the number itself, e.g. 28 = 1 + 2 + 4 + 7 + 14.

    The new discovery of the 45th Mersenne prime therefore means ipso facto the discovery of the 45th known perfect number.

    In later days Euler showed that Euclid's schema is the only schema for even perfect numbers. (Odd perfect numbers are an open question - it's known that there are none of 300 digits or less.)

    (For the record, numbers where the sum of factors falls short of the number - the majority - are called "deficient", numbers where the sum of factors exceeds the number are known as "abundant". The first abundant number is 12. Odd abundant numbers are possible, the smallest being 945.)

  25. John H Woods Silver badge


    >Just claim that 9.9999 recurring is not equal to 10, because the 9 is not 10

    >so there will be a very very very small difference.

    No difference whatsoever.

    >Then ask them if they also hold that 1.11111111 recurring in base 2

    >is equivalent to 10.

    No, it's equivalent to 2. Or 2r10

    There you go, no need for any mathematical sparks whatsoever. I am perfectly prepared to explain why zero point nine recurring is equal to 1 to any person who is curious. However, if they keep insisting I am wrong the conversation is over. It's pretty much the same with creationists, although to be fair they have a bigger chance of being right.

  26. Anonymous Coward
    Anonymous Coward

    @Sleeping Dragon,Andre Carneiro

    The point is knowlege for its own sake, our species wouldn't be where it is today if all scientific endeavor was based solely on short termism.

  27. Anonymous Coward

    optimus prime

    "...according to GIMPS protocol, the potential 45th Mersenne prime will not be officially disclosed until it has been verified as a prime... estimated completion on September 12 and September 16..."

    aw! - c'mon reg. how can you run this story now, knowing you'll leave us all at the end of our tethers with suspense til the middle of september. i know i shan't get a wink of sleep until i hear the outcome of the verification process!

  28. A J Stiles

    Better process for finding prime numbers

    If you want to find large prime numbers, you don't need a computer. Just a paruresis sufferer, a large quantity of supermarket own-brand diet lemonade and a toilet where the occupant can hear every sound outside.

  29. Paul Buxton


    "Mersenne prime + Large Hadron Collider = 10th September is end of the world."

    Well thank fuck for that. This will save me a load of hassle.

    Anyone who thinks infinity is a prime number is kidding themselves.

    Infinity/2 = Infinity

    Infinity/3 = Infinity

    Infinity/4 = Infinity

    Shall I go on?

    Or shall I get my coat?

  30. D
    Paris Hilton

    You can see why finding these numbers have such a cult following.

    No, I really can't.

    Paris because she'd rather suck dick than waste time on Mersenne Primes.

  31. Destroy All Monsters Silver badge

    We know that testing for primality is in P how many operations does it take to test this extra-large number? Or will testing be done probabilistically?

  32. MsJamie
    Black Helicopters


    LOL Probabilistically - in my sleep-addled state, I read that as Probaballistically, which would be something like the chance of getting shot...

  33. Sleeping Dragon
    Paris Hilton

    @ Peter Timon

    Oh really, does it solve World Peace? Can we generate 0-carbon electricity from this discovery?

    No? Then why bother?

    What's the point of discovering n th precision of a number or equation if it does nothing to preserve humanity or the world around us?

    You might as well collect stamps and count then number of Penny Blacks you have.

    Paris, because even she isn't such a waste of space.

  34. Anonymous Coward
    Anonymous Coward

    to Andre Carneiro

    "...I would be REALLY curious to know why millions of computer-hours were invested in THIS instead of something more obviously beneficial to mankind..."

    Well why not? Why did you invest a minute of your time posting a comment when you could have done something more beneficial. If a load of people want to crunch prime numbers for fun there's nothing wrong with that. Blimey, next you'll be outlawing music.

  35. Anonymous Coward

    Easiest way to prove 0.99999.. equal to 1

    For all the non-believers (tho most I'm hoping to be joking), the easiest way to prove 0.99999 recurring equals 1 is to consider how to represent it as a fraction.

    1/9 = 0.1111111111 recurring

    0.99999999 recurring = 9 * 0.11111111111 recurring.

    So you have 9 x 1/9 = 1.

    Or, more formally:

    x = 0.9999...

    10x = 9.9999...

    10x - x = 9.9999... - 0.9999...

    9x = 9

    x = 1

  36. adnim

    @Destroy All Monsters:We know what testing...

    Ask miss Jean Brody.

  37. Anonymous Coward

    Actually it's easier

    To know if a number N is prime, you only have to test numbers less than or equal to sqrt(N). And if you know all the primes up to that, it's a LOT easier, as you only need to test if the number is divisible by the primes less than or equal to sqrt(N). Granted, if you don't know the primes up to sqrt(N), it's a lot harder.

    It's very simple if you think about it.

    Finding primes is one of those problems that rapidly expands into however much computing power you can throw at it, If you know all primes up to M, you can start working on everything from M+1 to M^2, which gets large fast.

  38. Russell Howe

    GIMPS protocol

    Did they publish an RFC?

  39. Anonymous Coward
    Anonymous Coward

    re: actually it's easier

    So... what's the square root of (2^32,582,657)-1 then?... :-)

  40. Anonymous Coward
    Anonymous Coward

    @Sleeping Dragon

    How do you know it won't have some kind of obscure but crucial bearing on your (to you) more important projects?

    i don't suppose Einstein knew that his work would affect just about every aspect of our civilisation.

    Knowlege for its own sake doesn't need justification from anyone.

  41. Anonymous Coward

    You can't divide infinity by 2

    >Anyone who thinks infinity is a prime number is kidding themselves.

    >Infinity/2 = Infinity

    >I think you'll find that infinity is divisible by an infinite number of numbers.

    When talking about prime numbers, the work "divide" refers to the operation of integer division. This operation is definted on .... integers. "Infinity" isn't an integer. It isn't a rational number, it isn't an irrational number, it's not a real number, and it's not a complex number. So all three of the statements quotes above are basically nonsensical.

    There is of course a branch of mathematics called transfinite mathematics, which works with the different types of infinity - but anyone who works in that field will quite happily tell you that infinity is not a number. If you're engaged in a discussion of numbers, starting to talk about infinity will almost always result in confusion and error, unless it's clearly understood that any statement about infinity can be rewritten without using the term (e.g. "there are an infinite number of primes" -> "there is no integer which represents the total number of primes. When you think you've got them all, it's quite easy to prove there is at least one more".

  42. Tim Hoddy

    It's not that easy!

    This method doesn't work for numbers of the order of magnitude of, e.g. 9,808,358 digits denary.

    Where are you going to store all the primes less than the SQRT of this number?

  43. Andre Carneiro


    Dude, chill out! I'm not trying to outlaw anything!

    (Although RnB should be) ;)

    I was really just curious to find out if there was any particular application to this piece of knowledge that wasn't immediately obvious, that's all.

    And it's very kind to compare the value of one minute of my time to all those computer hours. I'm flattered. :P

  44. adnim

    infinities of all shapes and sizes

    A bit of a curiosity is infinity. There are infinite natural numbers; 1, 2, 3, 4, ... etc.

    There are infinite rational ( 1/4, 0.25) and irrational numbers (pi, sqrt 2)

    There are an infinite real numbers, values between 1 and 2, 2 and 3 etc.

    A set of all the real numbers is infinitely larger than the set of all rational numbers which is in turn infinitely larger than the set of all the natural numbers. It's elephants all the way down.

    Infinities come in different sizes.

  45. Chris Miller

    Prime testing

    This method - testing all the primes < SQRT(x) - is still (subject to a few tweaks) the most effective method for *factorising* a given number, at least until someone contructs a working quantum computer. There are much swifter techniques for testing if a number is prime * (particularly numbers of the form 2^p-1), so we are able to say "this number is not prime" without having any idea what its factors are.

    * some of the more efficient techniques are known to generate false negatives (very occasionally). So sometimes when you generate large primes (e.g. for use in RSA cryptography) one of the numbers may be only a pseudo-prime, in which case the encryption will fail. This happens rarely enough that the gains in speed are considered worthwhile compensation.

  46. John Savard

    Two corrections

    The previous record-holding Mersenne Prime wasn't 232,582,657 - 1, which would be an even number; it was (2 to the power of 32,582,687) minus one.

    Also, while Cantor's diagonal proof shows that there are more real numbers than there are natural numbers, the rational numbers and the natural numbers (or the integers) have the same cardinality.

  47. Anonymous Coward


    It's not "somewhat unique." It is actually unique. A thing is unique or it is not, period. There aren't any shades of grey.

  48. Anonymous Coward
    Paris Hilton

    Dividing by Zero

    Hey I just divided by zero. Oh Shi...

  49. Steve VanSlyck

    @Paul Buxton and @AC

    The end of the world is not in September. It is in December. 12/12/2012, to be precise. As to everybody else, .999 &c. clearly is equal to 1. I have Excel open right now and it says so right there.

  50. pctechxp

    I was a member of the world community grid

    and all I got was a lousy power bill!

  51. Kanhef

    @ adnim

    The sets of natural, whole, integer, and rational numbers all have the same size. The set of real numbers is larger. Infinite subsets of infinite sets (e.g. positive odd numbers, reals or rationals between 0 and 1) have the same size as their parent set.

  52. Qneiform

    "You can see why finding these numbers have such a cult following."

    While you are all being awesomely impressive mathmopedants, may I ask why "finding these numbers" is plural? Drop the "e" from "have" and it would be like Molesworth. And I don't mean the engineering formulae guy. And yes I can start a sentence with a conjunction. [Implodes.]

  53. Anonymous Coward

    Infinities of infinities

    Cantor's proposition of infinite cardinalities of infinities is still controversial. Personally I reckon that too sweeping a conclusion (confusion?) is drawn from Cantor's Diagonal Method and instead maintain my belief in the One And Only Infinity - and She isn't even signed.

  54. pctechxp

    It's the end of the world as we know it

    and I feel fine

    Mine's the one with a copy of the best of R.E.M. in the pocket

  55. Vic
    Paris Hilton

    um, no

    9.9 recurring is 10 for similar reasons to 1/0 being a number approaching infinity (ie exceedingly and unknowably large), right? Maths as less than applied was a long time ago...

    Although I'd have better chance of explaining to Paris that that latter one is true(ish) than to my daughter's fifth grade teacher who is absolutely adamant that 1/0=0. But then perhaps if someone just explained it and told her why you just don't introduce the concept of dividing by zero to smallish kids (did she never wonder why that was??) if you're not prepared to at least explain the idea behind it (dividing by an increasingly large number decreasing your solution increasingly and vice versa). The child refuses to try on the basis that (1) Teacher won't understand it and (2) on the offchance that she does, she (Teacher) will think she's an infernal knowitall and give her crap marks for maths for the rest of the year.

  56. Dr. Mouse

    @ Del Merritt

    OK, many have pointed out that the 44th Mersene prime was so close to 10 million digits that the 45th is likely to be over 10 million.

    Putting that aside, 9,808,358 to the nearest million is 10 million. Therefore you could quite easily argue that the 44th Mersene prime is approximately 10 million digits long.

  57. Michael H.F. Wilkinson Silver badge
    Paris Hilton

    Keep going

    There are infinite prime numbers, so they can keep on going forever finding bigger ones. I am not a number theorist, so I am not sure there are infinite Mersenne primes, but the proof for the infinite number of primes is simple:

    Assume that there are only N primes with N a finite number (however large). Now multiply all these N primes, and add one. The result is not divisible by ANY of the N primes. Therefore, it is either prime, or there exist some new prime number beyond those in the list of N primes. This contradicts the assumption that there exist only N primes. Therefore there are infinite prime numbers.

    Paris, because even she SHOULD be able to follow that.

  58. Phil Hare

    Every time GIMPS appears in the news...

    ...I always chcukle at the memory of a BBC Radio 4 documentary suggesting that if the listener wanted to take part in the search for primes they should type "GIMPS" in to a search engine.

    Ah, the innocence...

  59. Matt Devney


    All the discussion here is very interesting, but there's a very important point I think everyone's overlooked!

    George Woltman was on holiday. So:

    "the verification process didn't begin until the 26th. He estimates completion on September 12 and September 16."

    ON September 12 AND September 16 - are they not sure on the first date? Or do they check again on the 16th? Or does it depend on some sort of fractal alternate universe timing because reality has been warped by the computing power of these connected machines? Shall our universe implode if the 2 answers don't agree?

    Or is it a typo...? Naaah.

    And for those asking "why not find a cure to cancer instead?" - I'm not an expert (obviously) but I'm not sure that loads of computer CPUs churning through a load of numbers is the way to find such a cure. In fact, they're only really useful for this kind of abstract stuff.

    Please correct me if I'm wrong. Cheers!


  60. Dr Patrick J R Harkin

    9.9 recurring and 10

    They're not actually the same, it's just that there's no difference between them.

    That statement is either totally trite, or shows a deep understanding of mathematics. And I have no idea which.

  61. Hollerith

    equal to or equivalent?

    .999999 to 1, I mean.

  62. adnim


    I am not a mathematician, so will gracefully accept an error in my assumptions, but what about the irrational numbers between 1 and 2, 2 and 3, 3 and 4 ad infinitum, and not just zero and 1. Is a rational number not considered rational if it is greater than 1? Set theory is a void of ignorance for my part, so dumb in this area I most certainly am.

    On a less serious note, is infinity -1 an odd or an even number ;-)

  63. Anonymous Coward

    0.9r != 1

    Your 'proof' includes rounding errors in your division. There is no proof of 0.9r = 1 that isn't self fulfilling, therefore it may or may not be true.

  64. Anonymous Coward
    Paris Hilton

    1's and 0's ... my head hurts

    9.99... every time I move to the next 1/10th incriment along the decimal place line, the difference between 10 and 9.99... is an even smaller value than previously measured - as the spaces become even smaller it becomes increasingly more difficult to distinguish between the 9.99... and the 10. Presumably at some point, the difference becomes smaller than the numerical range to which it applies... and at that point it is no longer possible to identify any difference between 10 and 9.99... or is that between 9.99... and 10 - sorry, I got them mixed up.

    In physics the race to "absolute zero" holds an interesting analogy to wit: an ever increasing amount of energy must be expended in order to drop the temperature by an increasingly small amount - at present, if we consider London as 20 C (293.14 K) and New York as zero kelvin (-273.14 C) then we can currently get to within one pencil lead's width of the centre of New York ... but to take the next step would probably require an accident at the LHC. HOWEVER, in all seriousness, one pencil lead's width from the centre of New York is sufficient for physisisisisists to observe a complete breakdown of substance cohesion and of gravity - everything appears to become a superfluid, unbound by gravity - able to "flow" up and through anything, light drops to 37mph. Near enough to absolute zero for us to know what would happen should the final pencil lead's width be traversed. And my point is? 9.99... is so close to 10 that it is possible to know 10 without actually acheiving it.

    I prefer to consider that 1/0 = infinity (as opposed to "tends towards" infinity) - or, how many times can I remove nothing from 1? Obviously, every time I remove 0 from 1 there is still 1 left from which I can take another 0. There are 10 types of people, those who understand binary, and those who don't.

    Can anyone recall the proof that 1 = -1 ?

  65. William Old
    IT Angle

    I love these arguments...

    ... so I'm going to start a new one! :-)

    > A Mersenne number is a number that is one less than a power of two, or Mn = 2n – 1. So, the first few are 1, 3, 7, 15, 31, 63, and so on.

    No... the first few are 0, 1, 3, 7, 15, 31, 63, and so on. 2 to the power 0 is 1, so (2 to the power 0 minus 1) is 0. I'll leave it to the next poster to start arguing about the negative powers of 2... ;-)

  66. Anonymous Coward

    So what

    Like all those gold medals our muppets won at the freak show in China, what practical use has this now or in the future?

    Does it get us lower taxes, cheaper petrol, maybe it lowers the crime rate, speeds up the trains, keeps dickheads mobile phones switched off on the bus or maybe it, like the gold medals, means totally fuck all to anyone.

  67. Mike Fortey
    Paris Hilton

    Rusty maths

    My pure maths might be slightly rusty, but as I recall:

    9.9 reoccurring is not mathematically equal to 10 - It tends towards 10, as 10 - 1/infinity.

    However, as soon as you step outside pure mathematics, it does become 10. Or 'close enough for experimental purposes' as any scientist would say. If you aren't doing pure maths, it's 10, if not, it isn't.

    Prime numbers are worth hard cash and important because RSA public key encryption and the like generates keys by multiplying prime numbers. So the more primes that we have available means that there are more (and thus more secure) combinations - as far as I remember, anyhow.

    As for the 'unweildy to write' thing... well it isn't. If you read the article, a Mersenne prime is simply expressed as 2^blah -1.

    It isn't proven that this prime series is infinate. It might not be. That makes them interesting, too.

  68. Allan Hack-Barr
    Paris Hilton

    Infinite digit size?

    > the digits in the numbers quickly become extremely large

    Heyyy its the fonts!

    View > Text Size > Decrease

    Paris because she knows more about the size of digits than most.

  69. Anonymous Coward

    ...and faling

    2 to the power of infinity minus 1 to 1 against and falling..

    do not be alarmed - normality will be resumed as soon as we are sure what is normal anyway.

  70. Neil

    You can see why finding these numbers have such a cult following

    No, I really really can't.

  71. Anomalous Cowherd Silver badge

    Absolute Zero

    And the reason you can't cool an atom to absolute zero is it violates Heisenbergs Uncertainty principle. Temperature = the speed of the atom, absolute zero would imply it's stationary, and as you can't know both the location and velocity of a particle that's simply not on.

    Well I thought it was interesting.

  72. Anonymous Coward
    Thumb Up

    Reason for doing it?

    A lot of very talented academic have been promised a nice bucket of doh-ray-me, if they can get somewhere with this nonsense. So they rack a truck-load of kit up, give the problem and all wait. The number comes in, they win the money which they can then use to bugger off and hopefully do something far more useful with themselves!

  73. conan

    0.99999... is not equal to 1

    Look, 0.9999 recurring is not completely equal to 1, as otherwise their alphanumeric representation would be the same, but one of them clearly has a 0 and a point and some nines, and the other just has a 1. They're only mathematically equal, so to claim they are just "equal" is incorrect. Problem is, mathematicians always limit themselves to mathematics when discussing numbers.

  74. Mike Fortey


    "And the reason you can't cool an atom to absolute zero is it violates Heisenbergs Uncertainty principle."

    There was me thinking it was the Third Law of Thermodynamics.

    [The Second Law of Thermodynamics being that entropy in a system increases, and the First Law of Thermodynamics is: You do not talk about Thermodynamics.]

  75. Paul
    Paris Hilton

    RE: 1's and 0's ... my head hurts

    The difference between 9.99999... and 10 dose matter some times, but not to most people. It is best not to think about it to much, and as for the race to 0K, there are important things about being at 0.00001K and 0K, for example, as you say at very low temperatures odd things happen, at 0 nothing should happen. Any particle moving has energy, so therefore cannot be at 0K.

    and @Kanhef and adnim. You seem to be thinking of infinity as a definable number. It is a very difficult concept to get your head round I know (I can't) but one infinity cannot be bigger than another. Much like the concept of infinity -1, it just doesn’t work. The mistake you seem to be making is thinking rationally about infinity, when it is not a rational number.

    People so often make this mistake of trying to rationalise irrational numbers. It caused me allot of headaches trying to work with root -1, but ultimately you just have to accept that what you are doing works but you will never know why.

    People have written PhD's on the concept of infinity, or pi or root -1, and I am nowhere near that clever, but I hope that makes sence to you all.

    PH, because you should take her lead, as I have, and not think to hard.

  76. Anonymous Coward
    Anonymous Coward

    <no title>

    An infinitesimal can not be equal to zero, 'cause look I have an infinite number of infinitesimals in my pocket, here look; and see how much space they're taking up!

  77. D@v3

    45th Mersenne prime

    Im just hoping that the 45th Mersenne prime is somewhere in the region of 2^42,000,000-1

  78. Anonymous Coward
    Anonymous Coward


    You seem to be confusing equal with exactly equal.

    In maths 0.99999.... can be said to be equal to 1, but not exactly equal. It is just a way of stopping mathmatitions starting fights in the SU bar.

  79. Anonymous Coward
    Dead Vulture

    Urgh, my head hurts.

    I think I might go and search for Google on

  80. Joe M

    To all the cavemen!

    To all you "practically minded" morons who can't see the point: just because you are too lazy and stupid to find out about something does not mean that it's useless.

    Mersenne Primes and Sophie Germaine Primes and Lie Groups and Lagrangians and lots and lots of other "useless" mathematical entities will be out there, doing their work for us long after you miserable whingers have turned into forgotten dust.

    So my suggestion to all of you is to stop using your computers, turn off the lights, crawl back into your caves and start chipping some flint!

    (As for Austin Modine calling Marin Mersenne a nerd: too bad you don't allow strikethroughs in comments. I could put a few juicy, and much more fitting labels on you too.)

  81. Anonymous Coward

    @ paul

    at 0 nothing *should* happen ... indeed - roll on the LHC crew and what was that I read today about a lack of an "Environmental Impact Assessment" ? - LM(f)AO - anything to add Mark? (Not that I make a habit of saying, "I told you so" ... but this time I really did, 4 times - to your deaf ears.

    Hurrah, break out the lashings of ginger beer and hopefully next time you'll READ rather than just REACT.

  82. Anonymous Coward
    Paris Hilton

    0.9999 recurring -> 1

    It's not the maths that breaks down, it's the language.

  83. Anonymous Coward
    Anonymous Coward

    Elephants? E;ephants!?

    Adnim said: "...It's elephants all the way down..."

    Heretic! There are only 4 elephants! It's *turtles* all the way down!


  84. Stephen Gray

    @Joe M

    Good rant, more wrong than Neville Chamberlain was when he waved a piece of paper around but nonetheless a good rant

  85. Anonymous Coward
    Anonymous Coward

    @Phil Hare...

    That's nothing, a glass blowing friend of mine had just got his first internet connection when he needed to replace a piece of kit that goes between the furnace and the cooling oven. So without any fear, he loaded up google and typed in 'glory hole'.

    He hasn't done that since.

    PS I did enjoy 5 and another 5 numbers.

  86. Anonymous Coward
    Anonymous Coward

    answers on a postcard please

    What is 10-(9.9 recurring)?

  87. Michael H.F. Wilkinson Silver badge

    should the comment section be kept open...

    until there are 2^42,000,000-1 comments? That should set a record.

    BTW: 1 = 0 is easy to prove:

    consider the infinite series:

    k = 1 - 1 + 1 - 1 + 1 - 1 + 1 ..............................................

    No wadd them up in pairs and we have

    0 + 0 + 0 + 0 + 0 .................................

    which adds up to 0

    however, if we first remove the first 1 we have

    m = -1 + 1 - 1 + 1 - 1 + 1 ...........................................

    obviously m + 1 = k, or k - 1

    however, now add all the terms of m up in pairs: m = 0 + 0 + 0 + 0 +.............

    so m=0 and m+1 = k => k = 1

    combined with the first result we have 0 = 1

    it also follows that k - 1 = m and therefore - 1 = 0 = 1

    (anyone see where this goes wrong?)

  88. Anonymous Coward

    @Mike Fortey

    Getting just a little bit off-topic (!), but....

    "And the reason you can't cool an atom to absolute zero is it violates Heisenbergs Uncertainty principle.... There was me thinking it was the Third Law of Thermodynamics."

    TEMPERATURE is a measure of entropy measured on an ensemble. ATOMS only have temperature insofar as they have internal degrees of freedom (DOF), which have energies.

    Two ways to look at the minimum temperature, strictly greater than absolute zero:

    1) At least one internal DOF has an energy inversely Heisenberg-correspondent to the time you are observing it. Your observation time is limited to a photon of wavelength = radius of the universe.

    2) The universe is expanding and therefore "the edge" of the universe is "accelerating", and therefore has an event horizon. It emits Hawking radiation, of an astoundingly low temperature (photon has wavelength = radius of the universe), which the universe is bathed in. And those photons are too low a wavelength to be screened.

  89. Anonymous Coward
    Anonymous Coward

    nice one Michael

    ... but the "proof" I sought relies on square roots ...

    1/-1 = -1/1

    SqRoot (1/-1) = SqRoot (-1/1)

    SqRoot 1/SqRoot -1 = SqRoot -1/ SqRoot 1

    cross multiply to get...

    SqRoot 1 x SqRoot 1 = SqRoot -1 x SqRoot -1

    and therefore

    1 = -1

    and yes - it is equally flawed somewhere.

  90. Steve VanSlyck

    Thermodynamic Turtles


    >Heretic! There are only 4 elephants! It's *turtles* all the way down!

    One Turtle only, please. We don't need no stinking extra universes.

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