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

Felix Fröhlich felix.froe at gmail.com
Sat Feb 20 13:49:59 CET 2016


It should be 190000000000000000000000000000009 if I haven't made a mistake.
I let PARI create a string z of 32 zeros, then computed the smallest prime
of the form eval(Str(x, z, y)) for x from 1 to 19. I believe there can't be
a smaller one. While there are also primes with a single digit before the
string (like 300000000000000000000000000000029), they are all larger, since
their initial digit is larger than 1.

Regards
Felix

2016-02-20 9:57 GMT+01:00 Neil Sloane <njasloane at gmail.com>:

> I added a comment to A037053 saying that this is different (at n=32 for the
> first time) from the smallest prime with n consecutive zeros. What is the
> smallest prime with 32 consecutive zeros?  Could someone tell me, or better
> still, insert it in the new comment in A037053?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Sat, Feb 20, 2016 at 1:02 AM, Hans Havermann <gladhobo at teksavvy.com>
> wrote:
>
> > 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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> >
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> >
>
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