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Re: [PrimeNumbers] A prime dish in a prime base [SOLUTION]

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  • Alan Eliasen
    ... Spoiler space follows. . .. . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . . . . Sum in base 41843 is
    Message 1 of 16 , Sep 3, 2009
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      On 09/03/2009 02:40 AM, djbroadhurst wrote:
      > Suppose that we parse the string "cab", in base p, as
      > 12*p^2 + 10*p + 11. Then "cab" is a prime in the prime
      > base p = 41, where it evaluates to the decimal number 20593.
      >
      > Similarly, we may parse the incantation "abracadabra",
      > in base p, as 10*p^10 + 11*p^9 + 27*p^8 + 10*p^7 + 12*p^6 + 10*p^5
      > + 13*p^4 + 10*p^3 + 11*p^2 + 27*p + 10, which evaluates to the prime
      > 8510432846378191 in the prime base p = 31.
      >
      > The nonce-word "floccinaucinihilipilification" evaluates to the prime
      > 352402927208050896786973658273234894386040810340804173543364510421
      > in the prime base 199. For the meaning, see
      > http://www.worldwidewords.org/weirdwords/ww-flo2.htm
      >
      > Puzzle: Find the smallest prime base in which Aristophanes' dish
      > http://tinyurl.com/6xkeen
      > is prime, if we use O'Neill's tranliteration in line 1170 of
      > http://tinyurl.com/nnaqlk

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      Sum in base 41843 is
      9355934623362561735213219302693410823607868190849630269877\
      6553684917032146922567250080317347155330911049352272600264891303788077990113278\
      4853088920553317989172187911135472248955574815213603926445985233885389642117781\
      4381160736048159727697869729116763488380008580384563935286216104489332003841643\
      4760106323998198183345546437753307049885244185702893171182361757187414650365639\
      1793563743445464735466507739792305201194704747538514165228148227347542716827410\
      3317461237255320643879853668183786679561917227974652256331446555994563730135516\
      3026904731364993396280828241651057013994638897984779596310112725585193309862898\
      9978162623129572344332751322965737425155187359894442966740804307156470888035472\
      2453994844494330604029034206329792396426299163600028180427618021437461076507541\
      3062782241110381733982885164991797153719562713304314423


      --
      Alan Eliasen
      eliasen@...
      http://futureboy.us/
    • djbroadhurst
      ... gave a solution in agreement with [spoiler!] http://primes.utm.edu/curios/page.php?number_id=9432 More ambitiously, one might consider the 1185-letter word
      Message 2 of 16 , Sep 3, 2009
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        --- In primenumbers@yahoogroups.com, Alan Eliasen <eliasen@...>
        gave a solution in agreement with [spoiler!]
        http://primes.utm.edu/curios/page.php?number_id=9432

        More ambitiously, one might consider the 1185-letter word
        for the Tobacco Mosaic Virus, Dahlemense Strain, at
        http://www.fun-with-words.com/word_longest.html

        By my reckoning, this is probably prime in
        20 different prime bases less than 10^6.

        David
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