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

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• I did finally decide to restart this search, but it will still be Monday before I have (probably) ruled out the smaller interval.  I checked what you said,
Message 1 of 4 , Sep 14, 2013
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I did finally decide to restart this search, but it will still be Monday before I have (probably) ruled out the smaller interval.  I checked what you said, Jack, about ranges, and the heuristic probability of membership I crudely obtained that the desired number is in the 2nd one, assuming not in the one I am now checking, came out to about 10%, while the heuristic probability it is NOT in your larger range assuming it is not smaller is around 3.5%.   The chances of it not even being in the next range after that are astronomically small.
JGM

From: Jack Brennen <jfb@...>
To: James Merickel <moralforce120@...>
Sent: Tuesday, September 3, 2013 2:40 PM
Subject: Re: [PrimeNumbers] emirp all bases 2 through 14?

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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• No, mistaken about how long eliminating first range would take (another factor of 10), so that project is aborted.  Also, did not check just how small the
Message 2 of 4 , Sep 16, 2013
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No, mistaken about how long eliminating first range would take (another factor of 10), so that project is aborted.  Also, did not check just how small the heuristic probability of the number being in that range is.  Perhaps not so miniscule (like the next at around 10%).
JGM

----- Forwarded Message -----
From: James Merickel <moralforce120@...>
To: Jack Brennen <jfb@...>