Can anyone give me a simple explanation of what "Grahams number" is - I dont understand from Wiki?


Luis - Fantastic, I appreciate your work and will watch your videos. However my next question (and it was the second part I was referring to, not Benjamin Graham (however that will now be my next topic of reading). But Ramseys`s theory? And Mr Graham himself who I watched before asking this - said the simple summary was 7 and not 6....but your knowledge is above mine, so I will leave you to argue with Mr page:

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1 Answer

  • Luis
    Lv 6
    8 years ago
    Favorite Answer

    Dear Japanjef,

    Note that this number applies only to certain types of stocks in combination with a number of other criteria. The complete Graham selection procedure is much more elaborate. No decision should be made based on this number alone.

    The Graham number or Benjamin Graham number is a figure used in securities investing that measures a stock's so-called fair value. Named after Benjamin Graham, the founder of value investing, the Graham Number can be calculated as follows:

    Square root of (22.5 x (earning per share) x (book value per share))

    The final number is, theoretically, the maximum price that a defensive investor should pay for the given stock. Put another way, a stock priced below the Graham Number would be considered a good value.


    The World Champion largest number, listed in the latest Guinness Book of Records, is an upper bound, derived by R. L. Graham, from a problem in a part of combinatorics called Ramsey theory.

    Graham's number cannot be expressed using the conventional notation of powers, and powers of powers. If all the material in the universe were turned into pen and ink it would not be enough to write the number down. Consequently, this special notation, devised by Donald Knuth, is necessary.

    3^3 means '3 cubed', as it often does in computer printouts.

    3^^3 means 3^(3^3), or 3^27, which is already quite large: 3^27 = 7,625,597,484,987, but is still easily written, especially as a tower of 3 numbers: 333.

    3^^^3 = 3^^(3^^3), however, is 3^^7,625,597,484,987 = 3^(7,625,597,484,987^7,625,597,484,987), which makes a tower of exponents 7,625,597,484,987 layers high.

    3^^^^3 = 3^^^(3^^^3), of course. Even the tower of exponents is now unimaginably large in our usual notation, but Graham's number only starts here.

    Consider the number 3^^^...^^^3 in which there are 3^^^^3 arrows. A largish number!

    Next construct the number 3^^^...^^^3 where the number of arrows is the previous 3^^^...^^^3 number.

    An incredible, ungraspable number! Yet we are only two steps away from the original ginormous 3^^^^3. Now continue this process, making the number of arrows in 3^^^...^^^3 equal to the number at the previous step, until you are 63 steps, yes, sixty-three, steps from 3^^^^3. That is Graham's number.

    There is a twist in the tail of this true fairy story. Remember that Graham's number is an upper bound, just like Skewes' number. What is likely to be the actual answer to Graham's problem? Gardner quotes the opinions of the experts in Ramsey theory, who suspect that the answer is: 6

    Who am I, see my videos on Youtube

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