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

[Bob Selcoe]

Hans,

Thanks for the reply. After further consideration I agree with you and Robert Wilson.

I've posted some observations on https://oeis.org/A037053 to flesh out the ideas, publication pending.  Hopefully all is clear and I've made no calculation errors.

Cheers,
Bob S.


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From: "Hans Havermann" <gladhobo at teksavvy.com>
Sent: Saturday, February 20, 2016 12:02 AM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Smallest prime with a substring of exactly n zeros

> https://oeis.org/A037053 
> 
> There's already a conjecture there from Robert G. Wilson v suggesting the opposite (that two zero-substrings suffice). I tend to agree with that. The lengths of the second substring (for terms that require it) are relatively small compared to the lengths of the first. And (I think) we're only on the first of nine possible initial digits. It should be possible to estimate how many candidate numbers are available, given n, and multiply that with the probability of a number of that size being prime.
> 
>> On Feb 19, 2016, at 6:29 PM, Bob Selcoe <rselcoe at entouchonline.net> wrote:
>> 
>> It would be interesting to see if any terms have three or more substrings of zeros.  My guess is yes...
> 
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