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

Hans Havermann gladhobo at teksavvy.com
Sat Feb 20 07:02:01 CET 2016


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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