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

[Lucas Brown]

If my understanding of the time complexity of the operations is correct,
then I should have a definitive answer within a day.

On Tue, Jul 30, 2024 at 8:42 PM Neil Sloane <njasloane at gmail.com> wrote:

> 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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