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Re: [PrimeNumbers] Too big for any computer?

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  • Phil Carmody
    ... If by the number you mean 2^(3^53)+99, then clearly it isn t too big for any computer as it can trivially be represented using only 9 characters. It s
    Message 1 of 7 , Jun 9, 2009
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      --- On Tue, 6/9/09, Devaraj Kandadai <dkandadai@...> wrote:
      > I had  requested Ken (Kradenken)  to test whether  2^(3^53) + 99   is
      > eactly divisible by  107 or not.  He replied that
      > the number is too big for any computer.  Do you agree?

      If by "the number" you mean 2^(3^53)+99, then clearly it isn't too big for any computer as it can trivially be represented using only 9 characters. It's binary or decimal expansion is too big, but no-one's asking for its binary or decimal expansion, so that's irrelevant.

      To test whether it's divisible by 107 is trivial also, as 2^phi(107) == 1 (mod 107). So reduce 3^53 modulo phi(107):

      ? Mod(2,107)^lift(Mod(3,eulerphi(107))^53)+99
      Mod(0, 107)

      So indeed, it is divisible by 107.

      Phil
    • Norman Luhn
      I agree with Phil. Calculate 3^53,106 - 3 then 2^3+99 = 107 , 107 =0 mod 107 best ... Von: Phil Carmody Betreff: Re: [PrimeNumbers]
      Message 2 of 7 , Jun 9, 2009
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        I agree with Phil.

        Calculate 3^53,106 -> 3
        then 2^3+99 = 107 , 107 =0 mod 107

        best


        --- Phil Carmody <thefatphil@...> schrieb am Di, 9.6.2009:

        Von: Phil Carmody <thefatphil@...>
        Betreff: Re: [PrimeNumbers] Too big for any computer?
        An: "Prime Number" <primenumbers@yahoogroups.com>
        Datum: Dienstag, 9. Juni 2009, 16:37



















        --- On Tue, 6/9/09, Devaraj Kandadai <dkandadai@gmail. com> wrote:

        > I had  requested Ken (Kradenken)  to test whether  2^(3^53) + 99   is

        > eactly divisible by  107 or not.  He replied that

        > the number is too big for any computer.  Do you agree?



        If by "the number" you mean 2^(3^53)+99, then clearly it isn't too big for any computer as it can trivially be represented using only 9 characters. It's binary or decimal expansion is too big, but no-one's asking for its binary or decimal expansion, so that's irrelevant.



        To test whether it's divisible by 107 is trivial also, as 2^phi(107) == 1 (mod 107). So reduce 3^53 modulo phi(107):



        ? Mod(2,107)^lift( Mod(3,eulerphi( 107))^53) +99

        Mod(0, 107)



        So indeed, it is divisible by 107.



        Phil































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      • Alan Eliasen
        ... If you represent the numbers directly, then, yes, it s too big for any computer. However, I gave you a very short program the other day that shows a very
        Message 3 of 7 , Jun 9, 2009
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          Devaraj Kandadai wrote:
          > I had requested Ken (Kradenken) to test whether 2^(3^53) + 99 is
          > eactly divisible by 107 or not. He replied that the number is too big for
          > any computer. Do you agree?

          If you represent the numbers directly, then, yes, it's too big for
          any computer. However, I gave you a very short program the other day
          that shows a very simple way to test factors of large numbers like this
          using modular arithmetic. It could be trivially modified to answer this
          question, and test any number of factors that you chose for this or any
          of the other numbers that you've been asking about. I would suggest
          that you study it again, because it would help you answer repeated
          questions of this sort, and it would become a useful tool in your studies.

          Again, a suitable Frink program to exhaustively list the factors of
          your number is below: ( http://futureboy.us/frinkdocs/ ) If you have a
          recent version of Java installed, Frink is a one-click install from
          http://futureboy.us/frinkjar/frink.jnlp .

          Switch to programming mode (control-P) and paste in the following
          program. Hint: modPow[n,e,base] does (n^e) mod base, but does it
          efficiently without the numbers getting larger than base. Other
          languages should have a similar function, too, if you'd like to
          implement this in another language. You will be able to answer these
          and future similar questions easily if you understand how this program
          works.

          -------------------------------------------------
          e = 3^53
          n = 1
          while true
          {
          n = nextPrime[n]
          if (modPow[2,e,n] + 99) mod n == 0
          print[n + " "]
          }
          -----------------------------------------------------

          --
          Alan Eliasen
          eliasen@...
          http://futureboy.us/
        • Ken Davis
          Hi All, ... Hi All, In defence of my statement the original request was could I use pfgw on the number (2^(3^53)+99)/107 as Deva received an overflow in Pari I
          Message 4 of 7 , Jun 9, 2009
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            Hi All,
            --- In primenumbers@yahoogroups.com, Devaraj Kandadai <dkandadai@...> wrote:
            >
            > I had requested Ken (Kradenken) to test whether 2^(3^53) + 99 is
            > eactly divisible by 107 or not. He replied that the number is too big for
            > any computer. Do you agree?
            Hi All,
            In defence of my statement the original request was could I use pfgw on the number (2^(3^53)+99)/107 as Deva received an overflow in Pari
            I assumed a prp test was being requested.
            Hence my reply
            Cheers Ken
          • Ali Adams
            Peace All, Is there a given name to prime numbers that have prime digit sums? Example 67 and 6+7=13 If not can someone please suggest a short name if
            Message 5 of 7 , Jun 24, 2009
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              Peace All,

              Is there a given name to prime numbers that have prime digit sums?
              Example 67 and 6+7=13

              If not can someone please suggest a short name if possible.

               
              I really need to classify five different kinds of primes as shown below
              but the above case is the most urgent one please, thank you in advance.

              1) Prime with a prime digit sum
                  Example 67 and 6+7=13

              2) Prime with a prime digit sum recusively for all subsequent sums                       [Recusive Primes]
                  Example 47, 4+7=11 and 1+1=2
               
              3) Prime with prime digits
                  Example 37, 3 and 7

              4) Prime with prime digits and a prime digit sum
                  Example 337, 3, 3, 7 and 3+3+7=13

              5) Prime with prime digits and a prime digit sum recusively for all subsequent sums [Pure Primes]
                  Example 227, 2, 2, 7, 2+2+7=11, and 1+1=2


              Thank you all in advance and the most urgent one is kind (1) please.





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            • cino hilliard
              Maybe Sum Of Digits Is Prime - SODIP or SODIPS for more than one. So we have another name for additive primes in The Encyclopedia of Integer Sequences. An
              Message 6 of 7 , Jul 2, 2009
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                Maybe



                Sum Of Digits Is Prime - SODIP or SODIPS for more than one.
                So we have another name for "additive" primes in The Encyclopedia of Integer Sequences.

                An internet search has a lot of SODIP hits.

                So when you dip into the big bucket of primes if you dip just right or SODIP, you may draw
                sum of your primes schooner or ladle.

                Of course SODIP applies to all integers. I guess we could extend the name a little with
                SODOPIP. Ohoo.. the PIP part is exciting - Prime-Index-Primes. Now if we look for SODIPS
                for PIPS we have a new sequence.

                Enjoy,
                Suds Of Draught In Pint,
                Cino



                To: primenumbers@yahoogroups.com
                CC: pureprimes@...
                From: alipoland@...
                Date: Wed, 24 Jun 2009 07:20:22 -0700
                Subject: [PrimeNumbers] What is the name for this kind of primes







                Peace All,

                Is there a given name to prime numbers that have prime digit sums?
                Example 67 and 6+7=13

                If not can someone please suggest a short name if possible.


                I really need to classify five different kinds of primes as shown below
                but the above case is the most urgent one please, thank you in advance.

                1) Prime with a prime digit sum
                Example 67 and 6+7=13

                2) Prime with a prime digit sum recusively for all subsequent sums [Recusive Primes]
                Example 47, 4+7=11 and 1+1=2

                3) Prime with prime digits
                Example 37, 3 and 7

                4) Prime with prime digits and a prime digit sum
                Example 337, 3, 3, 7 and 3+3+7=13

                5) Prime with prime digits and a prime digit sum recusively for all subsequent sums [Pure Primes]
                Example 227, 2, 2, 7, 2+2+7=11, and 1+1=2

                Thank you all in advance and the most urgent one is kind (1) please.

                [Non-text portions of this message have been removed]










                [Non-text portions of this message have been removed]
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