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

[sven-h.simon at gmx.de]

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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