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 2008-07-12, 21:28 #1 KEP Quasi Admin Thing     May 2005 16608 Posts 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
 2008-07-12, 21:40 #2 michaf     Jan 2005 479 Posts 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 http://primes.utm.edu/prove/prove2_2.html for more reading material
2008-07-13, 00:26   #3
gd_barnes

May 2007
Kansas; USA

3·3,413 Posts

Quote:
 Originally Posted by michaf 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 http://primes.utm.edu/prove/prove2_2.html for more reading material
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.

Gary

Last fiddled with by gd_barnes on 2008-07-13 at 00:27

 2008-07-16, 10:53 #4 gd_barnes     May 2007 Kansas; USA 1023910 Posts 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 Last fiddled with by gd_barnes on 2008-07-16 at 21:11
 2008-07-16, 21:11 #5 gd_barnes     May 2007 Kansas; USA 1023910 Posts One k-value is now down for Sierp base 781: 346*781^4210+1 is prime. Gary Last fiddled with by gd_barnes on 2010-01-18 at 07:54 Reason: remove bases <= 500
 2008-07-19, 10:54 #6 gd_barnes     May 2007 Kansas; USA 27FF16 Posts Sierp base 781 k=370 is complete to n=10K. No primes. No more work to be done on it.
 2008-07-19, 14:11 #7 KEP Quasi Admin Thing     May 2005 24·59 Posts @ 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 and a slim hope of someday understanding Regards Kenneth! Last fiddled with by KEP on 2008-07-19 at 14:14
2008-07-19, 15:57   #8

Jan 2006
Hungary

22·67 Posts

Quote:
 Originally Posted by KEP Sierpinski base: 1023 1.: 13,61,1321 (covering no/yes?) k: 632462 Exponent: 6 Kenneth!
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.

2008-07-19, 16:22   #9
KEP

May 2005

24×59 Posts

Quote:
 Originally Posted by Siemelink 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.
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 Thanks for the info.

Kenneth!

2008-07-19, 16:38   #10

Jan 2006
Hungary

22×67 Posts

Quote:
 Originally Posted by KEP 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 Thanks for the info. Kenneth!
Oh, this is high school stuff. It is just a matter of having the right programs that give the output nicely.

Willem

2009-04-10, 21:05   #11
KEP

May 2005

24×59 Posts

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

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

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
Attached Files
 679_base_reservations.txt (3.3 KB, 328 views)

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