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

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• 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:

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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