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25364Re: [PrimeNumbers] emirp all bases 2 through 14?

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  • Jack Brennen
    Sep 3, 2013
      Heuristically, I think you'd expect to find the first
      number that is emirp in all bases 2 through 14 somewhere
      in the range between:

      Low = 5*6^20+157 (18280792200315037)
      High = 2*10^16-7 (19999999999999993)

      Clearly, that's a big range to search though -- and you'd
      have to eliminate the smaller permissible ranges first:

      Low = your finding (14322793967831)
      High = 6*9^13-1 (15251194969973)

      Low = 3*8^15+13 (105553116266509)
      High = 2*14^12-9 (113387824750583)

      (Heuristically, those ranges are unlikely to produce a
      solution -- but they should be checked of course.)

      Are there any more sophisticated sieving techniques which
      are easily applicable other than just a fast sieve for
      primes in the above ranges?



      On 9/3/2013 8:21 AM, James Merickel wrote:
      > I was able to get the first number that is emirp in all bases 2 through 13, 14322793967831 (decimal), but through base 14 is impossible with my resources. Maybe somebody else is interested. The base-13 result was lucky, being the solution through base 12.
      > JGM
      >
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