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-   -   Bases 501-1030 reservations/statuses/primes (https://www.mersenneforum.org/showthread.php?t=12994)

KEP 2008-07-12 21:28

Bases 501-1030 reservations/statuses/primes
 
@Garys edit: actually i'm now running a perfect test for base 781 sierpinski and it actually finds primes just the same as with bases below or equal 255. But if one take a look at the pfgwdoc.txt file, and looks under "-b" it states something with bases having to be between 2 and 255 :smile:

michaf 2008-07-12 21:40

That's the base it uses internaly to prove primality, it has nothing to do with the formula you are testing (No need to set it usually, it choses for you automagically...)

See [URL]http://primes.utm.edu/prove/prove2_2.html[/URL] for more reading material

gd_barnes 2008-07-13 00:26

[quote=michaf;137725]That's the base it uses internaly to prove primality, it has nothing to do with the formula you are testing (No need to set it usually, it choses for you automagically...)

See [URL]http://primes.utm.edu/prove/prove2_2.html[/URL] for more reading material[/quote]

Thanks for the info. Micha.

Based on that, test whatever base you want but please limit them to bases with somewhat low conjectured k-values. :smile:


Gary

gd_barnes 2008-07-16 10:53

KEP had mentioned testing base 781 with PFGW for primality proving. That got me curious because so many k's on this base have trivial factors. So I checked the conjecture of it and it is k=528 with a covering set of {17 23}.

Seeing that there were only ~120-130 k's that would need to be tested after eliminating all k==(1 mod 2), (2 mod 3), (4 mod 5), and (12 mod 13) that had trivial factors, I decided to give it a whirl.

It's not bad at all with just 2 k's remaining, k=346 & 370, at n=3K.

Based on this and my earlier test of k=4 on Sierp base 242 to n=3K, I will reserve all 3 of the k's on these 2 bases up to n=10K.


Gary

gd_barnes 2008-07-16 21:11

One k-value is now down for Sierp base 781:

346*781^4210+1 is prime.


Gary

gd_barnes 2008-07-19 10:54

Sierp base 781 k=370 is complete to n=10K. No primes.

No more work to be done on it.

KEP 2008-07-19 14:11

@ Willem and Gary: Excuse me for asking a ton of questions, but if it is not the covering sets (as I thought) that comes as output in the line saying something with "examining the primes in the covering set"(1) in the command line program, then what is it?

Example given:

Sierpinski base: 1023
1.: 13,61,1321 (covering no/yes?)
k: 632462
Exponent: 6

Hope it is clear what I asked, and also, if the "1." isn't the conjecture, the why is the covering.exe program only programmed to come up with a solution only and not a covering set on the same time?

My questions doesn't mean that I'll do any more conjectures, as stated earlier I doesn't have the skills, but they are simply out of curiosity :smile: and a slim hope of someday understanding :rolleyes:

Regards

Kenneth!

Siemelink 2008-07-19 15:57

[QUOTE=KEP;138014]
Sierpinski base: 1023
1.: 13,61,1321 (covering no/yes?)
k: 632462
Exponent: 6

Kenneth![/QUOTE]

A covering set means that there must be an elements of the set that divides 632462*1023^n+1, for any n. Occasionally there are more elements in that list than you strictly need. For this example you would have that

1321 divides 632462*1023^(3q+1)+1
61 divides 632462*1023^(3q+2)+1
13 divides 632462*1023^(3q+3)+1

covering all values of n.

Willem.

KEP 2008-07-19 16:22

[QUOTE=Siemelink;138018]A covering set means that there must be an elements of the set that divides 632462*1023^n+1, for any n. Occasionally there are more elements in that list than you strictly need. For this example you would have that

1321 divides 632462*1023^(3q+1)+1
61 divides 632462*1023^(3q+2)+1
13 divides 632462*1023^(3q+3)+1

covering all values of n.

Willem.[/QUOTE]

Ah now it all makes sence... but the above you state, just shows that it is in fact not for one with my mathematical skills to carry out such a search :smile: Thanks for the info.

Kenneth!

Siemelink 2008-07-19 16:38

[QUOTE=KEP;138019]Ah now it all makes sence... but the above you state, just shows that it is in fact not for one with my mathematical skills to carry out such a search :smile: Thanks for the info.

Kenneth![/QUOTE]

Oh, this is high school stuff. It is just a matter of having the right programs that give the output nicely.

Willem

KEP 2009-04-10 21:05

1 Attachment(s)
Hello

As part of my goal for this year, aswell in order to make sure my computer is not running idle while away on 3 weeks vacation some 4 weeks from now, I've decided to reserve 679 different Riesel bases with 1 thing in common, they all have k<=100K. All bases should be reported as completed in the end of this year. Also all bases will be tested to n=25K or proven. Already as I speak, 14 bases has been tested and 10 has been proven :smile:

This also means, that the Sierp base 63 reservation will still run, though it will only run in idle mode, so during nighttime and awaytime from the computer, the Sierpinski base 63 reservation will get full attention. Hope that everyone is alright with this new approach :smile:

Also I'll start by knooking down the riesel conjectures with the lowest predicted k-value.

Regards

KEP

Ps. Will frequently return my output results to Gary, as more and more bases gets completely proven or tested to n=25K


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