[seqfan] Re: Subject: Need help computing a number

[Lucas Brown]

I can now confirm that 340181 is the smallest exponent that yields a prime.

On Wed, Jul 31, 2024 at 6:21 AM Max Alekseyev <maxale at gmail.com> wrote:

> According to https://en.wikipedia.org/wiki/PrimeGrid the project Seventeen
> or Bust is still active.
>
> Regards,
> Max
>
> On Wed, Jul 31, 2024 at 5:22 AM SvenHSimon via SeqFan <
> seqfan at list.seqfan.eu>
> wrote:
>
> > Hello together,
> > as far I know the prime 104917*2^340181 was found in attempt to find the
> > smallest Riesel number in the same to find the smallest Sierpinski
> number.
> > These numbers will not be prime for any exponent m (104917*2^m-1 in the
> > case of Riesel, 2^m+1 for Sierpinski, who had that idea first as far I
> > know.). So there was a project like Mersenne prime search (named "17 or
> > bust" or so for Sierpinski numbers) to find a prime number and it was
> > sufficient to find any prime number. But technically they searched the
> > exponents from smallest to bigger ones and that was done for a lot of
> > years. They started with 17 numbers and as far I know there are only
> about
> > 5 remaining were the did not find a prime yet. So there is no proof, but
> it
> > is very likely that  104917*2^340181 is the smallest prime. Perhaps
> someone
> > involved in the project has more details, unfortunately the Mersenne
> forum
> > is behind a wall now, you have to register.
> >
> > Sven
> >
> > -----Ursprüngliche Nachricht-----
> > Von: SeqFan <seqfan-bounces at list.seqfan.eu> Im Auftrag von Neil Sloane
> > Gesendet: Mittwoch, 31. Juli 2024 05:42
> > An: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Betreff: [seqfan] Re: Subject: Need help computing a number
> >
> > PS
> >
> > (I had asked for the smallest m such that 104917*2^m - 1 is prime.)
> Thanks
> > to everyone who replied, especially Robert Gerbicz, who pointed to the
> web
> > page
> >
> >
> > Ray Ballinger and Wilfrid Keller, <a href="
> > http://www.prothsearch.com/rieselprob.html">The Riesel Problem:
> > Definition and Status</a>, Proth Search Page.
> >
> >
> > (already cited in A050412), and Ed Pegg, who found the web page
> >
> >
> >  https://rieselprime.de/ziki/Riesel_prime_2_104917
> >
> >
> > Both pages assert that 104917*2^340181 - 1 is prime. But it isn't clear
> >
> > whether m = 340181 is the /smallest/ m that gives a prime. The notation
> in
> > the second link is very unclear.  Can anyone clarify this?
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > Also Visiting Scientist, Math. Dept., Rutgers University,
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Tue, Jul 30, 2024 at 2:05 PM Neil Sloane <njasloane at gmail.com> wrote:
> >
> > > Dear Math Fun, Sequence Fans,
> > >
> > > Start with an integer k, 13 say, and repeatedly double it and add 1
> > > until reaching a prime:
> > >
> > > 13 -> 27 -> 55 -> 111 -> 223.
> > >
> > > This took 4 steps, so we set R(13) = 4. This is called Riesel's
> > > problem, and if we never reach a prime we set R(k) = 0. The sequence
> > R(k) is A050412.
> > > I think Riesel showed R(509203) = 0, and it seems it is believed that
> > > R(k) != 0 for k<509203.
> > >
> > > For another sequence (A374965) that Harvey Dale and I have been
> > > studying, we badly need the value of R(104916). Can someone help?  If
> > > 104916 takes m steps, the prime reached will be 104917*2^m - 1,
> > >
> > > so we don't actually need to see the prime (just m).
> > >
> > > I ran a naive Mathematica program (from A050412) on my iMAC, but I
> > > killed it after nearly 24 hours.
> > >
> > >  I have no idea how far it got.  The bottleneck is presumably the
> > > primality testing, but I don't know who has the fastest program for
> that.
> > > Best regards
> > > Neil
> > >
> > > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > > Also Visiting Scientist, Math. Dept., Rutgers University,
> > > Email: njasloane at gmail.com
> > >
> > >
> >
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> >
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