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Re: [PrimeNumbers] Re: anomalously large prime missing so far

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  • James Merickel
    Not sure anyone else is going to answer, but I would personally consider most of this to be a recreational challenge only, plus curiosity about the possibility
    Message 1 of 7 , Aug 5, 2011
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      Not sure anyone else is going to answer, but I would personally consider most of this to be a recreational challenge only, plus curiosity about the possibility of finding something pretty, at this point anyway. As a better example, I am now stuck on finding the first base-23 example of a non-trivial left-right concatenation of the first so many primes to be prime (as 23 is in base 10, this particular missing large number being, with this fact, the basis of a recent submission to Prime Curios!).
      Jim

      On Thu Aug 4th, 2011 12:49 PM EDT John wrote:

      >I probably sent this query to James rather than the group, so I will repeat the gist of it.
      >
      >Is the quest for series of numbers with what essentially is the property of having extraordinarily low factors a Critical Theoretical Question, of is it in the nature of finding very interesting, dare I say "merely" very interesting, facts?
      >
      >Practicality is by no means the touchstone of virtue, so I am not passing this search off as a vain endeavour, of course.
      >
      >I suppose this is to do with the nature of the mysteries of numbers. It seems to many mathematical musers that in a certian sense, there is an abundance of order and pattern in numbers (relating to primality and factorability), an abundance so great that it defies fathoming.
      >
      >Is that its charm, so obvious and, yet, so eluxive?
      >
      >--- In primenumbers@yahoogroups.com, James Merickel <merk7777777@...> wrote:
      >>
      >> I misjudged this to be a minor rarity, as remarked to me by Jens. Had intended a rejoinder for him after a calculation, but it turns out that no prime for placement of the 2-digit primes (through 11020 digits) is to be expected as reasonably possible at a level slightly larger than 1/4, removing essentially all interest.
      >> Jim
      >>
      >> On Sun Jul 31st, 2011 1:08 AM EDT James Merickel wrote:
      >>
      >> >Assuming that my PARI/GP did not crash, after 2, 23, 233, 2333 and 23333 are all prime, concatenation of n^2 copies of each prime prime(n) does not produce another prime (after adjoining any single copy of a prime) until some very large number. Just bringing this to the group's attention in the thought someone with a faster means of search is interested. I was/am planning to do a count of the number of primes among intermediate digit strings, so if someone does take this up I will search that instead and we can join notes and submit a curio together if the special prime sought after is found. Unless somebody knows how to break the program, unfortunately I can only give a time of about 5 days running on a Dell Studio XPS, much of the time with the CPU overtaxed, as information on where exactly in the search I am.
      >> >Jim
      >>
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      >
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