[seqfan] Re: Smallest prime with a substring of exactly n zeros
israel at math.ubc.ca
israel at math.ubc.ca
Fri Feb 19 17:18:48 CET 2016
If all the numbers of the form a(n zeros)b and 1(n zeros)ab are all
non-prime: a=1 to 9, b = 1,3,7,9, then the smallest prime with exactly n
zeros is most likely to be of the form 1(n-1 zeros)a0b. The first time that
happens is n=32, where if I haven't made a mistake A037053(32) =
10000000000000000000000000000000603.
Cheers,
Robert
On Feb 19 2016, Felix Fröhlich wrote:
>Dear Sequence fans
>
>a(n) is the smallest prime p containing a substring of exactly n zeros. The
>sequence (with offset 1) starts
>
>101, 1009, 10007, 100003, 1000003, 20000003, 100000007, 1000000007
>
>Does the sequence always coincide with A037053? A counterexample would have
>to be a prime having exactly n zeros in its decimal expansion but where
>those zeros do not form a contiguous string. That prime would also need to
>be the smallest prime with exactly n zeros. Does such a counterexample
>exist?
>
>Best regards
>Felix Fröhlich
>
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