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

[Max Alekseyev]

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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