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

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• ... 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/
• ... 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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