[seqfan] Re: Smallest prime with a substring of exactly n zeros

[israel at math.ubc.ca]

Yes. I now have a Maple program and b-file of 900 terms for A037053 (see 
draft edits), and indeed a(50) = 
10000000000000000000000000000000000000000000000500007. Up to n=900, all 
terms are either of the form a(n zeros)b or 1(n-k zeros)a(k zeros)b, the 
maximum k being 109 for A037053(808).

Cheers,
Robert

On Feb 19 2016, Hans Havermann wrote:

> Nice. Next candidates are n=43 which would end with 301; n=46, with 501; 
> and n=49, with 601. For n=50 the "1(n-1 zeros)a0b" form is not realized 
> in primes. Can we just shift zeros into the a-b slot and still get the 
> optimum answer? If so, n=50 would end (I think) with 500007.
>
>> On Feb 19, 2016, at 11:18 AM, israel at math.ubc.ca wrote:
>> 
>> 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.
>
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