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Re: [PrimeNumbers] Problem that should be solvable requiring scientific approach

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  • James Merickel
    Give example, but not that particular. Say our native base were 4 instead of 10. Then 2 won t work because although it stays 2 in translation from base 3, it
    Message 1 of 11 , Aug 6, 2011
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      Give example, but not that particular. Say our native base were 4 instead of 10. Then 2 won't work because although it stays 2 in translation from base 3, it becomes 4 in translation from base 2. 3 won't work because it immediately becomes 4. 5 in translation from base 3 to base 4 becomes 6, 7 becomes 9, 11 becomes 18, 13 becomes 21, 17 becomes 26, 19 becomes 33, 23 becomes 38, 29 becomes 66, 31 becomes 69, 37 becomes 81, 41 becomes 86, and finally 43 becomes 89. 89 in translation from base 2 to base 4 is 4417=7*631, so we have to continue even though 43 translates from base 2 to base 4 as our base-10 prime 1093, solving the base-4 analogue of the problem you thought it might be. Whatever the number for the base-4 analogue to my proposed problem is (and I could but won't rewrite that program right this minute), the translation of it from base 2 to base 4 need not be prime; the translation from base 2 to base 4 of the prime translation from base 3
      to base 4 needs to.
      Jim

      On Sat Aug 6th, 2011 8:33 PM EDT Jack Brennen wrote:

      >Okay, then I'm not following exactly the pattern that you're suggesting...
      >An example would probably do a lot of good. For instance, start with
      >the number 50006393431, and show where you go from there.
      >
      >Or does that not even work, because it's not a valid base-9 number
      >because of the 9 digit?
      >
      >On 8/6/2011 5:08 PM, James Merickel wrote:
      >> No. That is a different, much easier problem. The required number need not be prime in translation from bases 2 through 8 to base 10. It is sequential, rather than simultaneous, primality, and the reason for going down from 9 instead of up from 2 is to have intermediates more likely to be prime at smaller numbers and the end result be smaller. I expect the opposite order is probably unmanageable.
      >> Jim
      >>
      >> On Sat Aug 6th, 2011 8:00 PM EDT Jack Brennen wrote:
      >>
      >>> Is this what you are talking about?
      >>>
      >>> http://www.primepuzzles.net/puzzles/puzz_024.htm
      >>>
      >>>
      >>> If so, as you can see, that was solved 10 years ago. :)
      >>>
      >>>
      >>>
      >>> On 8/6/2011 4:07 PM, James Merickel wrote:
      >>>> This is one I worked on a little and will likely attack again in the reasonably near future if nobody else resolves it. I cannot guarantee that the very best programming will give an answer in a short enough time, but I can say with some certainty that being too casual won't. The problem is to find the first prime that translates by digital substitution from base 9 to base 10 as a prime, then the new number from base 8 to base 10 as a prime, and so on until a base 2 to base 10 translation yields a prime. To do this optimally requires a great deal of care with trial divisions. I believe I generated a few good through base 4 to base 10 by using a little but not much care, over a period of weeks.
      >>>> Jim
      >>>>
      >>>>
      >>>> ------------------------------------
      >>>>
      >>>> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      >>>> The Prime Pages : http://www.primepages.org/
      >>>>
      >>>> Yahoo! Groups Links
      >>>>
      >>>>
      >>>>
      >>>>
      >>>>
      >>>
      >>
      >>
      >>
      >
    • Kermit Rose
      ... Huh???? Please explain your translation calculations. 2 in base 3 is still 2. 2 in base 4 is still 2. 2 in base 2 is 10. 3 in base 2 is 11 3 in base 3 is
      Message 2 of 11 , Aug 7, 2011
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        >

        >3f. Re: Problem that should be solvable requiring scientific approach

        > Previously Posted by: "James Merickel" merk7777777@...
        > merk7777777

        > Date: Sat Aug 6, 2011 5:56 pm ((PDT))


        > Give example, but not that particular. Say our native base were 4
        > instead of 10. Then 2 won't work because although it stays 2 in
        > translation from base 3, it becomes 4 in translation from base 2.

        Huh???? Please explain your translation calculations.

        2 in base 3 is still 2.
        2 in base 4 is still 2.

        2 in base 2 is 10.

        3 in base 2 is 11
        3 in base 3 is 10



        > 3
        > won't work because it immediately becomes 4.

        3 in base 2 is 11
        3 in base 3 is 10


        5 in translation from
        > base 3 to base 4 becomes 6,

        5 in base 2 is 101
        5 in base 3 is 12
        5 in base 4 is 11


        > 7 becomes 9,

        7 in base 2 is 111
        7 in base 3 is 21
        7 in base 4 is 13
        7 in base 5 is 12
        7 in base 6 is 11
        7 in base 7 is 10


        > 11 becomes 18,

        11 in base 2 is 1011
        11 in base 3 is 102
        11 in base 4 is 23
        11 in base 5 is 21
        11 in base 6 is 15
        11 in base 7 is 14
        11 in base 8 is 13
        11 in base 9 is 12
        11 in base 10 is 11



        > 13 becomes
        > 21,

        13 in base 2 is 1101
        13 in base 3 is 111
        13 in base 4 is 31
        13 in base 5 is 23
        13 in base 6 is 21
        13 in base 7 is 16
        13 in base 8 is 15
        13 in base 9 is 14
        13 in base 10 is 13



        > 17 becomes 26, 19 becomes 33, 23 becomes 38, 29 becomes 66, 31
        > becomes 69, 37 becomes 81, 41 becomes 86, and finally 43 becomes 89.
        > 89 in translation from base 2 to base 4 is 4417=7*631, so we have to
        > continue even though 43 translates from base 2 to base 4 as our
        > base-10 prime 1093, solving the base-4 analogue of the problem you
        > thought it might be. Whatever the number for the base-4 analogue to
        > my proposed problem is (and I could but won't rewrite that program
        > right this minute), the translation of it from base 2 to base 4 need
        > not be prime; the translation from base 2 to base 4 of the prime
        > translation from base 3 to base 4 needs to.

        >Jim

        Please give examples of candidate solutions to your original stated
        problem, and how you either proved they were not solutions, or how you
        proved they were solutions.

        Kermit
      • James Merickel
        Okay. Consider that a) I thought it was rather poor reading to not see new number in the original as telling every last person here what the proposal was
        Message 3 of 11 , Aug 7, 2011
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          Okay. Consider that a) I thought it was rather poor reading to not see 'new number' in the original as telling every last person here what the proposal was and b) that nobody here immediately recognizes the base-4 representations of primes/composites but does immediately recognize all of them up to 100 in base 10. I had a feeling someone would do this. Thanks, but I guess I can assume you aren't really interested, Kermit.
          Jim

          On Sun Aug 7th, 2011 12:32 PM EDT Kermit Rose wrote:

          > >
          >
          > >3f. Re: Problem that should be solvable requiring scientific approach
          >
          > > Previously Posted by: "James Merickel" merk7777777@...
          > > merk7777777
          >
          > > Date: Sat Aug 6, 2011 5:56 pm ((PDT))
          >
          >
          > > Give example, but not that particular. Say our native base were 4
          > > instead of 10. Then 2 won't work because although it stays 2 in
          > > translation from base 3, it becomes 4 in translation from base 2.
          >
          >Huh???? Please explain your translation calculations.
          >
          >2 in base 3 is still 2.
          >2 in base 4 is still 2.
          >
          >2 in base 2 is 10.
          >
          >3 in base 2 is 11
          >3 in base 3 is 10
          >
          >
          >
          > > 3
          > > won't work because it immediately becomes 4.
          >
          >3 in base 2 is 11
          >3 in base 3 is 10
          >
          >
          >5 in translation from
          > > base 3 to base 4 becomes 6,
          >
          >5 in base 2 is 101
          >5 in base 3 is 12
          >5 in base 4 is 11
          >
          >
          > > 7 becomes 9,
          >
          >7 in base 2 is 111
          >7 in base 3 is 21
          >7 in base 4 is 13
          >7 in base 5 is 12
          >7 in base 6 is 11
          >7 in base 7 is 10
          >
          >
          > > 11 becomes 18,
          >
          >11 in base 2 is 1011
          >11 in base 3 is 102
          >11 in base 4 is 23
          >11 in base 5 is 21
          >11 in base 6 is 15
          >11 in base 7 is 14
          >11 in base 8 is 13
          >11 in base 9 is 12
          >11 in base 10 is 11
          >
          >
          >
          > > 13 becomes
          > > 21,
          >
          >13 in base 2 is 1101
          >13 in base 3 is 111
          >13 in base 4 is 31
          >13 in base 5 is 23
          >13 in base 6 is 21
          >13 in base 7 is 16
          >13 in base 8 is 15
          >13 in base 9 is 14
          >13 in base 10 is 13
          >
          >
          >
          > > 17 becomes 26, 19 becomes 33, 23 becomes 38, 29 becomes 66, 31
          > > becomes 69, 37 becomes 81, 41 becomes 86, and finally 43 becomes 89.
          > > 89 in translation from base 2 to base 4 is 4417=7*631, so we have to
          > > continue even though 43 translates from base 2 to base 4 as our
          > > base-10 prime 1093, solving the base-4 analogue of the problem you
          > > thought it might be. Whatever the number for the base-4 analogue to
          > > my proposed problem is (and I could but won't rewrite that program
          > > right this minute), the translation of it from base 2 to base 4 need
          > > not be prime; the translation from base 2 to base 4 of the prime
          > > translation from base 3 to base 4 needs to.
          >
          > >Jim
          >
          >Please give examples of candidate solutions to your original stated
          >problem, and how you either proved they were not solutions, or how you
          >proved they were solutions.
          >
          >Kermit
          >
          >
          >
          >
          >
          >
        • Jack Brennen
          ... you should expect to be questioned about exactly what you re talking about. You didn t write a single base 2 or base 4 representation anywhere, and
          Message 4 of 11 , Aug 7, 2011
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            When you write things like:

            > 89 in translation from base 2 to base 4 is 4417=7*631

            you should expect to be questioned about exactly what you're talking about.

            You didn't write a single base 2 or base 4 representation anywhere, and expecting people to fill in the blanks is just asking for misunderstandings.

            How about this:
            89 (base 10) is equal to 1011001 (base 2)
            1011001 (base 4) is equal to 4417 (base 10)

            Looking back at all of your emails on this subject, I can't find any places where you write things in a representation other than base 10, which is kind of funny considering that the problem
            depends entirely on non-base-10 representations of numbers.

            I suppose I'd restate your original problem like this:

            Take a starting number A_0.

            Write A_0 in base 9, and treat the string as a base 10 representation, yielding A_1.
            Write A_1 in base 8, and treat the string as a base 10 representation, yielding A_2.
            Write A_2 in base 7, and treat the string as a base 10 representation, yielding A_3.
            Write A_3 in base 6, and treat the string as a base 10 representation, yielding A_4.
            Write A_4 in base 5, and treat the string as a base 10 representation, yielding A_5.
            Write A_5 in base 4, and treat the string as a base 10 representation, yielding A_6.
            Write A_6 in base 3, and treat the string as a base 10 representation, yielding A_7.
            Write A_7 in base 2, and treat the string as a base 10 representation, yielding A_8.

            Find A_0 such that A_0 through A_8 are all prime.



            On 8/7/2011 12:45 PM, James Merickel wrote:
            > Okay. Consider that a) I thought it was rather poor reading to not see 'new number' in the original as telling every last person here what the proposal was and b) that nobody here immediately recognizes the base-4 representations of primes/composites but does immediately recognize all of them up to 100 in base 10. I had a feeling someone would do this. Thanks, but I guess I can assume you aren't really interested, Kermit.
            > Jim
            >
            > On Sun Aug 7th, 2011 12:32 PM EDT Kermit Rose wrote:
            >
            >>>
            >>
            >>> 3f. Re: Problem that should be solvable requiring scientific approach
            >>
            >>> Previously Posted by: "James Merickel" merk7777777@...
            >>> merk7777777
            >>
            >>> Date: Sat Aug 6, 2011 5:56 pm ((PDT))
            >>
            >>
            >>> Give example, but not that particular. Say our native base were 4
            >>> instead of 10. Then 2 won't work because although it stays 2 in
            >>> translation from base 3, it becomes 4 in translation from base 2.
            >>
            >> Huh???? Please explain your translation calculations.
            >>
            >> 2 in base 3 is still 2.
            >> 2 in base 4 is still 2.
            >>
            >> 2 in base 2 is 10.
            >>
            >> 3 in base 2 is 11
            >> 3 in base 3 is 10
            >>
            >>
            >>
            >>> 3
            >>> won't work because it immediately becomes 4.
            >>
            >> 3 in base 2 is 11
            >> 3 in base 3 is 10
            >>
            >>
            >> 5 in translation from
            >>> base 3 to base 4 becomes 6,
            >>
            >> 5 in base 2 is 101
            >> 5 in base 3 is 12
            >> 5 in base 4 is 11
            >>
            >>
            >>> 7 becomes 9,
            >>
            >> 7 in base 2 is 111
            >> 7 in base 3 is 21
            >> 7 in base 4 is 13
            >> 7 in base 5 is 12
            >> 7 in base 6 is 11
            >> 7 in base 7 is 10
            >>
            >>
            >>> 11 becomes 18,
            >>
            >> 11 in base 2 is 1011
            >> 11 in base 3 is 102
            >> 11 in base 4 is 23
            >> 11 in base 5 is 21
            >> 11 in base 6 is 15
            >> 11 in base 7 is 14
            >> 11 in base 8 is 13
            >> 11 in base 9 is 12
            >> 11 in base 10 is 11
            >>
            >>
            >>
            >>> 13 becomes
            >>> 21,
            >>
            >> 13 in base 2 is 1101
            >> 13 in base 3 is 111
            >> 13 in base 4 is 31
            >> 13 in base 5 is 23
            >> 13 in base 6 is 21
            >> 13 in base 7 is 16
            >> 13 in base 8 is 15
            >> 13 in base 9 is 14
            >> 13 in base 10 is 13
            >>
            >>
            >>
            >>> 17 becomes 26, 19 becomes 33, 23 becomes 38, 29 becomes 66, 31
            >>> becomes 69, 37 becomes 81, 41 becomes 86, and finally 43 becomes 89.
            >>> 89 in translation from base 2 to base 4 is 4417=7*631, so we have to
            >>> continue even though 43 translates from base 2 to base 4 as our
            >>> base-10 prime 1093, solving the base-4 analogue of the problem you
            >>> thought it might be. Whatever the number for the base-4 analogue to
            >>> my proposed problem is (and I could but won't rewrite that program
            >>> right this minute), the translation of it from base 2 to base 4 need
            >>> not be prime; the translation from base 2 to base 4 of the prime
            >>> translation from base 3 to base 4 needs to.
            >>
            >>> Jim
            >>
            >> Please give examples of candidate solutions to your original stated
            >> problem, and how you either proved they were not solutions, or how you
            >> proved they were solutions.
            >>
            >> Kermit
            >>
            >>
            >>
            >>
            >>
            >>
            >
            >
            >
            > ------------------------------------
            >
            > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
            > The Prime Pages : http://www.primepages.org/
            >
            > Yahoo! Groups Links
            >
            >
            >
            >
            >
          • James Merickel
            Jack, I disagree with your first sentence. In what bases we use normally (not hard since there is really only one option) does the digit 9 exist? Do you
            Message 5 of 11 , Aug 7, 2011
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              Jack, I disagree with your first sentence. In what bases we use normally (not hard since there is really only one option) does the digit 9 exist? Do you recognize 89 as being the first prime in that base in that chain of calculations. We wouldn't even be here if you had read the first post carefully, with the 'new number' referred to there being the prime translation of an original from base 9 to base 10. I get it from a standpoint of writing to literature, but nobody here is attempting that because some is essentially meaningless formality and some things that might not be assumed we should be able to here.
              Jim

              On Sun Aug 7th, 2011 8:23 PM EDT Jack Brennen wrote:

              >When you write things like:
              >
              >> 89 in translation from base 2 to base 4 is 4417=7*631
              >
              >you should expect to be questioned about exactly what you're talking about.
              >
              >You didn't write a single base 2 or base 4 representation anywhere, and expecting people to fill in the blanks is just asking for misunderstandings.
              >
              >How about this:
              > 89 (base 10) is equal to 1011001 (base 2)
              > 1011001 (base 4) is equal to 4417 (base 10)
              >
              >Looking back at all of your emails on this subject, I can't find any places where you write things in a representation other than base 10, which is kind of funny considering that the problem
              >depends entirely on non-base-10 representations of numbers.
              >
              >I suppose I'd restate your original problem like this:
              >
              > Take a starting number A_0.
              >
              > Write A_0 in base 9, and treat the string as a base 10 representation, yielding A_1.
              > Write A_1 in base 8, and treat the string as a base 10 representation, yielding A_2.
              > Write A_2 in base 7, and treat the string as a base 10 representation, yielding A_3.
              > Write A_3 in base 6, and treat the string as a base 10 representation, yielding A_4.
              > Write A_4 in base 5, and treat the string as a base 10 representation, yielding A_5.
              > Write A_5 in base 4, and treat the string as a base 10 representation, yielding A_6.
              > Write A_6 in base 3, and treat the string as a base 10 representation, yielding A_7.
              > Write A_7 in base 2, and treat the string as a base 10 representation, yielding A_8.
              >
              > Find A_0 such that A_0 through A_8 are all prime.
              >
              >
              >
              >On 8/7/2011 12:45 PM, James Merickel wrote:
              >> Okay. Consider that a) I thought it was rather poor reading to not see 'new number' in the original as telling every last person here what the proposal was and b) that nobody here immediately recognizes the base-4 representations of primes/composites but does immediately recognize all of them up to 100 in base 10. I had a feeling someone would do this. Thanks, but I guess I can assume you aren't really interested, Kermit.
              >> Jim
              >>
              >> On Sun Aug 7th, 2011 12:32 PM EDT Kermit Rose wrote:
              >>
              >>>>
              >>>
              >>>> 3f. Re: Problem that should be solvable requiring scientific approach
              >>>
              >>>> Previously Posted by: "James Merickel" merk7777777@...
              >>>> merk7777777
              >>>
              >>>> Date: Sat Aug 6, 2011 5:56 pm ((PDT))
              >>>
              >>>
              >>>> Give example, but not that particular. Say our native base were 4
              >>>> instead of 10. Then 2 won't work because although it stays 2 in
              >>>> translation from base 3, it becomes 4 in translation from base 2.
              >>>
              >>> Huh???? Please explain your translation calculations.
              >>>
              >>> 2 in base 3 is still 2.
              >>> 2 in base 4 is still 2.
              >>>
              >>> 2 in base 2 is 10.
              >>>
              >>> 3 in base 2 is 11
              >>> 3 in base 3 is 10
              >>>
              >>>
              >>>
              >>>> 3
              >>>> won't work because it immediately becomes 4.
              >>>
              >>> 3 in base 2 is 11
              >>> 3 in base 3 is 10
              >>>
              >>>
              >>> 5 in translation from
              >>>> base 3 to base 4 becomes 6,
              >>>
              >>> 5 in base 2 is 101
              >>> 5 in base 3 is 12
              >>> 5 in base 4 is 11
              >>>
              >>>
              >>>> 7 becomes 9,
              >>>
              >>> 7 in base 2 is 111
              >>> 7 in base 3 is 21
              >>> 7 in base 4 is 13
              >>> 7 in base 5 is 12
              >>> 7 in base 6 is 11
              >>> 7 in base 7 is 10
              >>>
              >>>
              >>>> 11 becomes 18,
              >>>
              >>> 11 in base 2 is 1011
              >>> 11 in base 3 is 102
              >>> 11 in base 4 is 23
              >>> 11 in base 5 is 21
              >>> 11 in base 6 is 15
              >>> 11 in base 7 is 14
              >>> 11 in base 8 is 13
              >>> 11 in base 9 is 12
              >>> 11 in base 10 is 11
              >>>
              >>>
              >>>
              >>>> 13 becomes
              >>>> 21,
              >>>
              >>> 13 in base 2 is 1101
              >>> 13 in base 3 is 111
              >>> 13 in base 4 is 31
              >>> 13 in base 5 is 23
              >>> 13 in base 6 is 21
              >>> 13 in base 7 is 16
              >>> 13 in base 8 is 15
              >>> 13 in base 9 is 14
              >>> 13 in base 10 is 13
              >>>
              >>>
              >>>
              >>>> 17 becomes 26, 19 becomes 33, 23 becomes 38, 29 becomes 66, 31
              >>>> becomes 69, 37 becomes 81, 41 becomes 86, and finally 43 becomes 89.
              >>>> 89 in translation from base 2 to base 4 is 4417=7*631, so we have to
              >>>> continue even though 43 translates from base 2 to base 4 as our
              >>>> base-10 prime 1093, solving the base-4 analogue of the problem you
              >>>> thought it might be. Whatever the number for the base-4 analogue to
              >>>> my proposed problem is (and I could but won't rewrite that program
              >>>> right this minute), the translation of it from base 2 to base 4 need
              >>>> not be prime; the translation from base 2 to base 4 of the prime
              >>>> translation from base 3 to base 4 needs to.
              >>>
              >>>> Jim
              >>>
              >>> Please give examples of candidate solutions to your original stated
              >>> problem, and how you either proved they were not solutions, or how you
              >>> proved they were solutions.
              >>>
              >>> Kermit
              >>>
              >>>
              >>>
              >>>
              >>>
              >>>
              >>
              >>
              >>
              >> ------------------------------------
              >>
              >> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
              >> The Prime Pages : http://www.primepages.org/
              >>
              >> Yahoo! Groups Links
              >>
              >>
              >>
              >>
              >>
              >
            • John
              You say: *I get it from a standpoint of writing to literature, but nobody here is attempting that because some is essentially meaningless formality and some
              Message 6 of 11 , Aug 7, 2011
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                You say:

                *I get it from a standpoint of writing to
                literature, but nobody here is attempting that because some is essentially
                meaningless formality and some things that might not be assumed we should be
                able to here.*

                Mathematical grammar and syntax are extremely formal, which is one of the reasons that, except you have learnt in the halls of institutes of learning, or by choosing somehow the best texts to learn from, Mathematicians and academics talk only themselves on their chosen specialty. A non mathematician normally will not be heeded as he is regarded as one or more of the following:
                (1) an intruder
                (2) a nut
                (3) too lazy to learn
                (4) too trivial
                (5) too stupid

                All of which keeps the standards up, and gets rid of distractions.

                But, you are not being asked by any of them to explain. The tolerably intelligent non academics permitted here are the ones talking to you. And we want to understand you.

                We even know what it is to have an intuition and not be able to express it.

                But you, pal, are to but it bluntly not making sense.

                So, why not go right back, sit down, and try put yoursel in the mind of the listener, understand where is *coming from* and where he is *at*. Then we might learn something.

                However, even from the standpoint of *normal* syntax, meaning everyday speech, there is a certain limited


                --- In primenumbers@yahoogroups.com, James Merickel <merk7777777@...> wrote:
                >
                > Jack, I disagree with your first sentence. In what bases we use normally (not hard since there is really only one option) does the digit 9 exist? Do you recognize 89 as being the first prime in that base in that chain of calculations. We wouldn't even be here if you had read the first post carefully, with the 'new number' referred to there being the prime translation of an original from base 9 to base 10. I get it from a standpoint of writing to literature, but nobody here is attempting that because some is essentially meaningless formality and some things that might not be assumed we should be able to here.
                > Jim
                >
                > On Sun Aug 7th, 2011 8:23 PM EDT Jack Brennen wrote:
                >
                > >When you write things like:
                > >
                > >> 89 in translation from base 2 to base 4 is 4417=7*631
                > >
                > >you should expect to be questioned about exactly what you're talking about.
                > >
                > >You didn't write a single base 2 or base 4 representation anywhere, and expecting people to fill in the blanks is just asking for misunderstandings.
                > >
                > >How about this:
                > > 89 (base 10) is equal to 1011001 (base 2)
                > > 1011001 (base 4) is equal to 4417 (base 10)
                > >
                > >Looking back at all of your emails on this subject, I can't find any places where you write things in a representation other than base 10, which is kind of funny considering that the problem
                > >depends entirely on non-base-10 representations of numbers.
                > >
                > >I suppose I'd restate your original problem like this:
                > >
                > > Take a starting number A_0.
                > >
                > > Write A_0 in base 9, and treat the string as a base 10 representation, yielding A_1.
                > > Write A_1 in base 8, and treat the string as a base 10 representation, yielding A_2.
                > > Write A_2 in base 7, and treat the string as a base 10 representation, yielding A_3.
                > > Write A_3 in base 6, and treat the string as a base 10 representation, yielding A_4.
                > > Write A_4 in base 5, and treat the string as a base 10 representation, yielding A_5.
                > > Write A_5 in base 4, and treat the string as a base 10 representation, yielding A_6.
                > > Write A_6 in base 3, and treat the string as a base 10 representation, yielding A_7.
                > > Write A_7 in base 2, and treat the string as a base 10 representation, yielding A_8.
                > >
                > > Find A_0 such that A_0 through A_8 are all prime.
                > >
                > >
                > >
                > >On 8/7/2011 12:45 PM, James Merickel wrote:
                > >> Okay. Consider that a) I thought it was rather poor reading to not see 'new number' in the original as telling every last person here what the proposal was and b) that nobody here immediately recognizes the base-4 representations of primes/composites but does immediately recognize all of them up to 100 in base 10. I had a feeling someone would do this. Thanks, but I guess I can assume you aren't really interested, Kermit.
                > >> Jim
                > >>
                > >> On Sun Aug 7th, 2011 12:32 PM EDT Kermit Rose wrote:
                > >>
                > >>>>
                > >>>
                > >>>> 3f. Re: Problem that should be solvable requiring scientific approach
                > >>>
                > >>>> Previously Posted by: "James Merickel" merk7777777@...
                > >>>> merk7777777
                > >>>
                > >>>> Date: Sat Aug 6, 2011 5:56 pm ((PDT))
                > >>>
                > >>>
                > >>>> Give example, but not that particular. Say our native base were 4
                > >>>> instead of 10. Then 2 won't work because although it stays 2 in
                > >>>> translation from base 3, it becomes 4 in translation from base 2.
                > >>>
                > >>> Huh???? Please explain your translation calculations.
                > >>>
                > >>> 2 in base 3 is still 2.
                > >>> 2 in base 4 is still 2.
                > >>>
                > >>> 2 in base 2 is 10.
                > >>>
                > >>> 3 in base 2 is 11
                > >>> 3 in base 3 is 10
                > >>>
                > >>>
                > >>>
                > >>>> 3
                > >>>> won't work because it immediately becomes 4.
                > >>>
                > >>> 3 in base 2 is 11
                > >>> 3 in base 3 is 10
                > >>>
                > >>>
                > >>> 5 in translation from
                > >>>> base 3 to base 4 becomes 6,
                > >>>
                > >>> 5 in base 2 is 101
                > >>> 5 in base 3 is 12
                > >>> 5 in base 4 is 11
                > >>>
                > >>>
                > >>>> 7 becomes 9,
                > >>>
                > >>> 7 in base 2 is 111
                > >>> 7 in base 3 is 21
                > >>> 7 in base 4 is 13
                > >>> 7 in base 5 is 12
                > >>> 7 in base 6 is 11
                > >>> 7 in base 7 is 10
                > >>>
                > >>>
                > >>>> 11 becomes 18,
                > >>>
                > >>> 11 in base 2 is 1011
                > >>> 11 in base 3 is 102
                > >>> 11 in base 4 is 23
                > >>> 11 in base 5 is 21
                > >>> 11 in base 6 is 15
                > >>> 11 in base 7 is 14
                > >>> 11 in base 8 is 13
                > >>> 11 in base 9 is 12
                > >>> 11 in base 10 is 11
                > >>>
                > >>>
                > >>>
                > >>>> 13 becomes
                > >>>> 21,
                > >>>
                > >>> 13 in base 2 is 1101
                > >>> 13 in base 3 is 111
                > >>> 13 in base 4 is 31
                > >>> 13 in base 5 is 23
                > >>> 13 in base 6 is 21
                > >>> 13 in base 7 is 16
                > >>> 13 in base 8 is 15
                > >>> 13 in base 9 is 14
                > >>> 13 in base 10 is 13
                > >>>
                > >>>
                > >>>
                > >>>> 17 becomes 26, 19 becomes 33, 23 becomes 38, 29 becomes 66, 31
                > >>>> becomes 69, 37 becomes 81, 41 becomes 86, and finally 43 becomes 89.
                > >>>> 89 in translation from base 2 to base 4 is 4417=7*631, so we have to
                > >>>> continue even though 43 translates from base 2 to base 4 as our
                > >>>> base-10 prime 1093, solving the base-4 analogue of the problem you
                > >>>> thought it might be. Whatever the number for the base-4 analogue to
                > >>>> my proposed problem is (and I could but won't rewrite that program
                > >>>> right this minute), the translation of it from base 2 to base 4 need
                > >>>> not be prime; the translation from base 2 to base 4 of the prime
                > >>>> translation from base 3 to base 4 needs to.
                > >>>
                > >>>> Jim
                > >>>
                > >>> Please give examples of candidate solutions to your original stated
                > >>> problem, and how you either proved they were not solutions, or how you
                > >>> proved they were solutions.
                > >>>
                > >>> Kermit
                > >>>
                > >>>
                > >>>
                > >>>
                > >>>
                > >>>
                > >>
                > >>
                > >>
                > >> ------------------------------------
                > >>
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                > >> The Prime Pages : http://www.primepages.org/
                > >>
                > >> Yahoo! Groups Links
                > >>
                > >>
                > >>
                > >>
                > >>
                > >
                >
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