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:

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=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

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

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

346*781^4210+1 is prime.


Gary

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

No more work to be done on it.

@ 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!

[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.

[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!

[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

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

[quote=KEP;168818]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[/quote]


All I can say is, good luck. You'll need it.

For that many bases, it will take a large chunk of time just to show them on the pages and I don't want to spent an inordinate amount of time checking them. Therefore, I expect the following:

1. Remove all k's that are multiples of the base where k-1 is prime.

2. Remove all k's that contain algebraic factors, show which k's are removed, and show why they do in a manner at least somewhat consistent with my pages. You have to get the math down pat on this! You might check the algebraic factors thread to see the pattern of how many of them occur.

3. Analyze all bases that are perfect powers of smaller base(s). Check the k's for the smaller base(s) that have already been searched for primes and search limits. You may need to send Emails to me or to projects to find out about this. Example: Base 1024 will have primes that can be converted from bases 2 (perfect 10th power), 4, (perfect 5th power), and 32 (perfect square). This can get more complex than base 25.

Kenneth, just pick 3-4 bases that have already been started and take them higher like I've done with bases 22 and 28 or Riesel bases 75 and 80. Alternatively like I've done with some of the Sierp bases < 100, take 3-4 bases at a time and take your time analyzing each one to make sure nothing is missed.

Why continue choosing such humongous and difficult efforts? I don't get it.


Gary

1. There shouldn't be many k that are multiples of the base where k-1 is prime, since a majority of the larger k conjectures has high bases, hence multiplication will very fast make an conjectural overflow

2. Since not many k's will remain once I test further than n=2500, then srsieve will remove those with algebraic factors, and keep those k's that doesn't has algebraic factors, so that should also be possible to show which ones is removed as a result of algebraic factors.

3. This might be more complex, however I'll look into what I can do here, though I'm not strong on the math of that particular area.

I did choose this, because I would really like to see someday that all base less than 2^10 has been taken to at least n=25K, and my personal goal was to see if this could be done for any bases where k<=100K before the end of 2009 :smile: So thats why plain and simple.

Kenneth!

[QUOTE=gd_barnes;168823]All I can say is, good luck. You'll need it.

For that many bases, it will take a large chunk of time just to show them on the pages and I don't want to spent an inordinate amount of time checking them. Therefore, I expect the following:

1. Remove all k's that are multiples of the base where k-1 is prime.

2. Remove all k's that contain algebraic factors, show which k's are removed, and show why they do in a manner at least somewhat consistent with my pages. You have to get the math down pat on this! You might check the algebraic factors thread to see the pattern of how many of them occur.

3. Analyze all bases that are perfect powers of smaller base(s). Check the k's for the smaller base(s) that have already been searched for primes and search limits. You may need to send Emails to me or to projects to find out about this. Example: Base 1024 will have primes that can be converted from bases 2 (perfect 10th power), 4, (perfect 5th power), and 32 (perfect square). This can get more complex than base 25.

Kenneth, just pick 3-4 bases that have already been started and take them higher like I've done with bases 22 and 28 or Riesel bases 75 and 80. Alternatively like I've done with some of the Sierp bases < 100, take 3-4 bases at a time and take your time analyzing each one to make sure nothing is missed.

Why continue choosing such humongous and difficult efforts? I don't get it.


Gary[/QUOTE]

OK, suit yourself. Good luck.

What you are proposing would likely take a person with 2 quads many years and possible a decade or more to accomplish with current software at current computer speeds. But obviously I'm not going to convince you.

When estimating things, which is required for setting realistic goals, you should take the most difficult task first, divide it up into as many smaller pieces as possible, and see how long all of those smaller pieces combined will take. Then determine how many tasks there are that are close to as difficult as the one that is most difficult, multiply that by the time to do the most difficult one, go on to "medium" difficult tasks, do the same, etc.

Here is a thought: Find a base > 500 in your list that is not divisible by 3, is not b=2^q-1 (because those are the most prime), and that has a conjecture of k>~50000. See how long this base takes you to test it up to n=10000 and then report back how many k's are remaining, how long it will take to test that entire base up to n=25000, and how realistic your goal is. I am 100% sure that you will be unpleasantly surprised.

Kenneth, I'm not going to keep responding trying to get you to reserve smaller and less difficult pieces of work. I've tried my best but for some reason, you simply refuse to take the time necessary to properly estimate things before reserving them.

Srsieve will not remove k's that contain partial algebraic factors that make a full covering set. It will only tell you that you have SOME k/n pairs with algebraic factors that can be removed but that doesn't mean that ALL of the k/n pairs can be removed. The latter is a necessary condition for actually removing the k's from testing. Your statement about srsieve means that you clearly don't get the math. This is a math forum and this project can be quite math-intensive when starting new bases. I'll be glad to help you with the math involved but it has to be for a reasonable-sized reservation. I won't help at all with 674 bases, even if only 10-20 of them have k's with partial algebraic factors that make a full covering set. Sometimes I've spent up to 2 hours getting the algebraic factors correct on just one base. I've even found algebraic factors well after testing had gone on past n=25K, which wasted quite a bit of CPU time. After spending many hours at it, I've now generallized a lot of them (there's a thread about it) so it's not nearly as difficult to find them. That said, there are still many exceptions which pop up and are not easy to spot.

Just report whatever you complete and I'll show it on my pages IF the work is correct. If it is not, I won't and will return it to you to fix it with only a cursory explanation. If you're going to reserve huge amounts of work, you have to get all of the work right with little assistance. If you're willing to be more realistic and reserve 3-4 bases at a time like everyone else does, I'll be glad to help you with some of the trickier ones.

Only time will convince you how unrealistic your goal is.


Gary

@ Gary: OK, I'll still start up with the bases with the lowest k-values since they appear to be easily taken up to n=25K or even more easily proven. Since you're willing to allow me to not take the entire 679 bases to n=25K or proven, then I'll exclude all those bases where SRsieve tells me that there is partial algebraric factors. Doing it this way, most likely also means, that I'm not going to spend as much time working on the bases as I thought, and it might mean that I'm actually going to unreserve those bases that I've not computed any work on as soon as I return from vacation.

At the moment there is currently 33 proven bases where there is prime for all k's less than the conjectured k. However there will get to be loads more since there is still remaining conjectures with a conjectured lower k-value of 4. Aswell there is many with a lower conjectured k-value of 6 and 8 etc. However it can not be completely ruled out that some of these lower conjectures will be hard to take to n=25K, for their final remaining k.

Kenneth

[quote=KEP;168894]@ Gary: OK, I'll still start up with the bases with the lowest k-values since they appear to be easily taken up to n=25K or even more easily proven. Since you're willing to allow me to not take the entire 679 bases to n=25K or proven, then I'll exclude all those bases where SRsieve tells me that there is partial algebraric factors. Doing it this way, most likely also means, that I'm not going to spend as much time working on the bases as I thought, and it might mean that I'm actually going to unreserve those bases that I've not computed any work on as soon as I return from vacation.

At the moment there is currently 33 proven bases where there is prime for all k's less than the conjectured k. However there will get to be loads more since there is still remaining conjectures with a conjectured lower k-value of 4. Aswell there is many with a lower conjectured k-value of 6 and 8 etc. However it can not be completely ruled out that some of these lower conjectures will be hard to take to n=25K, for their final remaining k.

Kenneth[/quote]


Kenneth,

Please read your Email. There are numerous problems with what you have sent me. I don't have time to review and fix everything before showing it on the pages so you need to correct it and send it back.

After sending back the corrections, please stop this effort entirely and focus on bases 3 and 63. Base 63 by itself will take multiple CPU years to test to n=25K and so would easily keep your machines busy while you are gone. Heck, the sieving for n<131072 by itself should keep 8 cores busy for at least 3 weeks. It's simple enough to split up the P-ranges on multiple cores and tell srsieve to output factors in a manner similar to what sr2sieve does such that they can be removed from the main file.

When you get back from your trip, then perhaps we can talk about specifically 3-5 bases that you can work on. If you finish those in 2 days, then we can do the same with another 3-5 bases. There's little reason to reserve so much at once, even if you do have big goals.


Gary

@ Gary: I've read your e-mail and replyed. I will follow your advice and leave the startups to someone who actually understands the basics.

Kenneth

@ All:

I am unreserving my hundreds of Riesel reservations, since my computers is now guarenteed to be busy while on vacation, to someone else except the following Riesel base:

999 n=10000 (87 k's remaining)

Regards

Kenneth

Ps. Following bases is proven (not yet send to Gary): 259, 519, 649, 714, 844 and base 989 has k=2 remaining at n=25K

Kenneth,

Thanks for the udpate. Before I left on my last business trip 9 days ago, I updated the pages for many of your bases. I still have about 30 of them yet to list where the conjecture is k=4 and that you have proven.

Since base 989 is not proven, can you please forward me your results file when you get back?


Thanks,
Gary

Riesel Base 704
 

Reserving Riesel Base 704 n=25K-40K

Riesel Base 704 complete from n=25K-40K - Nothing found

Results emailed

Riesel Base 704 released

(Obviously I forgot to reserve it BEFORE I ran it, DUH)

Below are some bases where b==(1 mod 30) with conjectures <=1000 that I've tested up to n=2500. I chose these because these are typically very primes bases for their size. A little over half were proven. More details are shown on the web pages.

Riesel base/conjecture/k's remain
571; k=12; proven
601; k=818; 50, 120, 300, 482, 624, & 744
781; k=254; 50
811; k=260; 8 & 258
901; k=12; proven
961; k=38; proven

Sierp base/conjecture/k's remain
571; k=12; proven
601; k=216; proven
811; k=552; 252, 358, 378, 450, 510, & 538
901; k=12; proven
961; k=1000; 316, 508, 586, 630, 636, 688, 766, 778, 820, 846, 886, & 892


For now I'm not reserving any of these but I likely will later take the ones that have k's remaining to n=10K if other people haven't done so at that point.


Gary

50*781^3112-1 is prime!
I'll take Riesel 811 to 10k. Edit: k=8 has no primes to 10k, PFGWing k=258 now...

[quote=Mini-Geek;194577]PFGWing k=258 now...[/quote]
Also no primes to n=10k. Unreserving Riesel 811.

Riesel Base 989
 

tested just for fun the remaining k=2 from n=25000 and found this:

Primality testing 2*989^26868-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 23, base 8+sqrt(23)
Calling Brillhart-Lehmer-Selfridge with factored part 54.54%
[b]2*989^26868-1 is prime![/b] (873.8538s+0.0080s)

so this is my first proven base (very small one but a beginning :grin:)

[quote=kar_bon;195325]tested just for fun the remaining k=2 from n=25000 and found this:

Primality testing 2*989^26868-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 23, base 8+sqrt(23)
Calling Brillhart-Lehmer-Selfridge with factored part 54.54%
[B]2*989^26868-1 is prime![/B] (873.8538s+0.0080s)

so this is my first proven base (very small one but a beginning :grin:)[/quote]

Personally I would "give credit" for a base as "proven" if the final prime is n>10K so there you go, you got one! Well done. Below that and it just becomes "not particularly exciting" or noteworthy. Otherwise KEP and I would have tons of bases proven, most with a highest prime of n<100.

One thing of interest about this base: Although there are many bases with a conjecture of k=4 that are proven with only a prime for k=2, this is the 1st such base proven with a prime at n>250. The current bases proven by finding only a prime for k=2 at n>100 are:

Riesel base 989, n=26868
Riesel base 779, n=220
Riesel base 629, n=186
Riesel base 449, n=174
Riesel base 29, n=136


All bases where b==(29 mod 30) will have a conjecture of k=4 on both sides and will only need to be tested for k=2 because odd k's will have a trivial factor of 2. Afaik, all of the Riesel bases <= 1024 have been done but most of the higher Sierp bases have not been. If anyone wants to take on the task of doing some of them, most can be done almost instantly and will have a prime at n<10. If you decide to do this, please let me know ahead of time. Most will likely test very quickly but multiple bases take quite a while to add to the pages even for a small conjecture. I'll want to know which bases so I can start adding them to the pages before getting all of the info.

Edit: There is only one such Riesel base <= 1024 remaining to be proven. The highest one: base 1019, which has currently been tested to n=25K. So there you go Karsten...another possible one to prove. Doing so would prove all Riesel bases <= 1024 where b==(29 mod 30). :-)


Gary

I'll take Sierp. base 961 to 50K, for starters.

Sierp. base 961 around 15K; 3 primes, 9 to go.

[quote=Batalov;195547]Sierp. base 961 around 15K; 3 primes, 9 to go.[/quote]

I can't change the testing limit on the pages without a listing of the primes found. I'll just leave it at n=2500 for now.

I'll take Riesel base 811.

[B]Riesel base 811[/B] is proven:
[FONT=Arial Narrow]8*811^31783-1 is 3-PRP! (189.6443s+0.0104s)
258*811^28010-1 is 3-PRP! (179.3691s+0.0093s)[/FONT]
[FONT=Arial Narrow][/FONT]
[FONT=Arial Narrow]Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FFT length 32K on 8*811^31783-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
8*811^31783-1 is prime! (2419.9390s+0.0107s)[/FONT]

[FONT=Arial Narrow]Running N+1 test using discriminant 3, base 3+sqrt(3)
Special modular reduction using zero-padded FFT length 48K on 258*811^28010-1[/FONT]
...running... will let you know if it's not prime. :rolleyes:

Great work Serge. Another one bites the dust! :smile:

Those b==(1 mod 30) bases sure are prime.

I am running a lot of odd high bases, just to get a feeling.
I will carefully catalog what's there, and the ranges and result files, but for now, some cleared k's to include into the webpage:

[FONT=Arial Narrow]508*31^7188+1 is 3-PRP! (1.4761s+0.0008s) <== that's Sierp base 961[/FONT]
[FONT=Arial Narrow]586*31^15728+1 is 3-PRP! (6.6518s+0.0013s)[/FONT]
[FONT=Arial Narrow]636*31^8674+1 is 3-PRP! (2.3250s+0.0008s)[/FONT]
[FONT=Arial Narrow]120*601^4663-1 is 3-PRP! (4.1509s+0.0024s)[/FONT]
[FONT=Arial Narrow]378*811^6792+1 is 3-PRP! (7.5817s+0.0011s)[/FONT]

[quote=Batalov;195674][B]Riesel base 811[/B] is proven:
[FONT=Arial Narrow]8*811^31783-1 is 3-PRP! (189.6443s+0.0104s)[/FONT]
[FONT=Arial Narrow]258*811^28010-1 is 3-PRP! (179.3691s+0.0093s)[/FONT] :rolleyes:[/quote]

An amazing note about this proof:

This is only the 3rd base proven with TWO primes of n>25K and the very 1st Riesel base! The other two are Sierp bases 11 and 23, the latter of which is the only one with two primes of n>100K.

What's so remarkable is that the base is 35X larger than any previous base with this attribute! :smile:

There is only one k remaining on 9 bases that would end up having 3 or more primes of n>25K if we can get them proven. They are Riesel bases 22, 23, 27, 49, and 72 and Sierp bases 9, 10, 17, and 33.

If proven, Riesel base 22 would have 5 primes of n>25K and Sierp base 17 would have 4. All the rest above would have 3. Sierp base 17 would be the 1st one with 3 primes of n>100K!


Gary

Reserving Riesel 1019 to 50K, and Riesel 1021 to 40K.

Riesel base 704 is proven
 

A big fish. (176,647 digits)

[B]2*704^62034-1[/B] is 3-PRP! (605.8170s+0.0069s)
[FONT=Arial Narrow]Done.
PFGW Version 20090928.Win_Dev (Beta 'caveat utilitor') [GWNUM 25.13][/FONT]
[FONT=Arial Narrow]Output logging to file ../BR704a.txt
No factoring at all, not even trivial division
Primality testing 2*704^62034-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FFT length 48K on 2*704^62034-1
N+1: 2*704^62034-1 15000/586809 mro=0.052734375...[/FONT]
...a few hours later will submit to Top5000.

Congratulations on a large proof Serge! :smile:

doing some work on riesel base 1017 at the minute conjectured k is 900.

I took Sierp. base 1002 (conj. k=1240) and apart from GFNs at k=1 and k=base, there are 10 k's left at 9.8K:
152 154 171 409 448 492 613 707 917 1106
I'll make a "Chris"-like zip file for every base, Gary, sometime this weekend.

[QUOTE=gd_barnes;195333]Edit: There is only one such Riesel base <= 1024 remaining to be proven. The highest one: base 1019, which has currently been tested to n=25K. So there you go Karsten...another possible one to prove. Doing so would prove all Riesel bases <= 1024 where b==(29 mod 30). :-)
[/QUOTE]

k=2 for Riesel Base 1019 at n=63.4k and continuing!

Riesel Base 1002 is proven with conj. k=237.
Primes are attached.

[quote=Batalov;197034]I took Sierp. base 1002 (conj. k=1240) and apart from GFNs at k=1 and k=base, there are 10 k's left at 9.8K:
152 154 171 409 448 492 613 707 917 1106
I'll make a "Chris"-like zip file for every base, Gary, sometime this weekend.[/quote]

Serge,

This is a tremendous number of new bases and I have to check them all and subsequently update the pages, which I'm close to finishing now. The problem that I'm having is that I make it a rule to not list k's remaining until I can balance them; that is I have all of the primes. What I must have is a listing of the primes for n>2500 (preferrably n>1000). The biggest problem are the ones like the above where you're listing no primes or only primes for n>5000 (or 7000 or 10000). For those, I have to ignore them on the pages or make a note to myself to follow up on them. I have spare cores on a slower machine and can fairly quickly use it to test to n=2500 without sieving. But to test to n=5000 or 10000 to get that complete listing would require that I stop other efforts, sieve, and then test...too much personal time and CPU resources.

It would really help me out if you would post primes n>2500 and k's remaining at the same time. Otherwise I have to update the pages twice or just ignore the 1st posting of k's remaining, which means someone else may end up testing a base that you have already started on.

For now, I'm going to list what I can on the pages with a note to myself to follow up on primes needed for n=2500 to (the lower limit of what you're listing shows). In the future, I won't show them at all until I get the n>2500 primes, which means a base or two could get missed.


Thanks,
Gary

Riesel base 1000 proven
 

Hi all,

The riesel conjecture 12 for base 1000 is proven.
k = 1, 4, 7, 10 are eliminated because 1000-1 has 3 as a factor.
k = 8 can be eliminated because

All k = m^3 for all n; factors to (m*10^n - 1) *(m^2*100^n + m*10^n + 1)
( I stole this from base 27)

That leaves these primes:
2*1000^1-1
3*1000^1-1
5*1000^1-1
6*1000^998-1
9*1000^1-1
11*1000^3-1

Willem.

Sierp base 1000
 

Sierp Base 1000
Conjectured k = 12

Found Primes:[CODE]3*1000^1+1
4*1000^1+1
6*1000^3+1
7*1000^1+1
9*1000^1+1[/CODE]

Remaining k's: Tested to n=10K
10*1000^n+1

Trivial Factor Eliminations:
2
5
8
11

GFN Eliminations:
1

Base Released

(If k=10 can be eliminated for some algebraic/trivial reason, I don't see why. The automatic PFGW script didn't eliminate it and it's not a cube. It is equivalent to 10^(3*n+1)+1, but I don't know if that implies anything terribly interesting.)

Riesel base 701
 

Riesel Base 701
Conjectured k = 14

Found Primes:[code]2*701^2-1
4*701^1-1
10*701^31-1
12*701^2-1
[/code]Trivial Factor Eliminations:
6
8

Conjecture Proven

Riesel Base 707
Conjectured k = 14

Found Primes:[code]2*707^350-1
4*707^3-1
6*707^1-1
8*707^4-1
10*707^1-1
[/code]Remaining k's: Tested to n=2500
12*707^n-1

Base Released

Riesel Base 713
 

Riesel Base 713
Conjectured k = 8

Found Primes:[code]2*713^2-1
4*713^1-1
6*713^2-1[/code]

Conjecture Proven

[QUOTE=Mini-Geek;198183]Sierp Base 1000
Conjectured k = 12

Found Primes:[CODE]3*1000^1+1
4*1000^1+1
6*1000^3+1
7*1000^1+1
9*1000^1+1[/CODE]

Remaining k's: Tested to n=10K
10*1000^n+1

Trivial Factor Eliminations:
2
5
8
11

GFN Eliminations:
1

Base Released

(If k=10 can be eliminated for some algebraic/trivial reason, I don't see why. The automatic PFGW script didn't eliminate it and it's not a cube. It is equivalent to 10^(3*n+1)+1, but I don't know if that implies anything terribly interesting.)[/QUOTE]

That would be a GFN prime for base=10, so it is very unlikely that there is a prime. (probably we know only: 10^(2^n)+1 is prime for n=0,1).

Riesel Base 716
Conjectured k = 238

Found Primes:[code]3*716^2-1
4*716^5-1
5*716^14-1
7*716^1-1
8*716^2-1
9*716^3-1
10*716^1-1
13*716^27-1
15*716^1-1
17*716^2-1
18*716^51-1
19*716^3-1
20*716^78-1
22*716^11-1
24*716^1-1
25*716^3-1
28*716^1-1
30*716^3-1
32*716^228-1
33*716^1-1
35*716^2-1
37*716^39-1
39*716^9-1
42*716^1-1
43*716^5-1
44*716^4-1
47*716^8-1
48*716^1-1
49*716^1-1
50*716^2-1
52*716^11-1
54*716^44-1
55*716^7-1
57*716^5-1
58*716^915-1
59*716^22-1
60*716^2-1
62*716^6-1
63*716^5-1
64*716^1-1
65*716^670-1
68*716^6-1
69*716^26-1
70*716^1-1
72*716^1-1
73*716^1-1
74*716^6-1
75*716^1-1
77*716^2-1
80*716^8-1
82*716^1-1
83*716^2-1
84*716^2-1
85*716^1-1
87*716^6-1
88*716^167-1
90*716^1-1
93*716^1-1
94*716^29-1
97*716^265-1
98*716^216-1
99*716^283-1
102*716^3-1
103*716^5-1
104*716^4-1
108*716^2-1
110*716^150-1
112*716^1-1
113*716^4-1
114*716^18-1
115*716^1-1
119*716^2-1
120*716^2-1
124*716^7-1
125*716^100-1
127*716^1-1
128*716^30-1
129*716^1-1
130*716^15-1
132*716^3-1
135*716^10-1
137*716^2-1
138*716^1-1
139*716^1-1
140*716^80-1
142*716^97-1
143*716^20-1
145*716^3-1
147*716^1-1
148*716^1-1
149*716^6-1
150*716^4-1
152*716^96-1
153*716^1-1
154*716^145-1
158*716^2-1
159*716^1-1
160*716^5-1
162*716^7-1
163*716^1-1
164*716^2-1
165*716^3-1
167*716^2-1
168*716^42-1
169*716^11-1
172*716^3-1
173*716^2-1
174*716^2-1
175*716^1-1
178*716^1-1
180*716^1-1
182*716^20-1
184*716^1-1
185*716^4-1
187*716^313-1
189*716^17-1
192*716^2-1
193*716^419-1
195*716^1-1
197*716^52-1
198*716^1-1
202*716^9-1
203*716^16-1
204*716^1-1
205*716^7-1
207*716^26-1
208*716^1-1
212*716^12-1
213*716^5-1
214*716^5-1
215*716^22-1
217*716^1-1
218*716^4-1
219*716^4-1
220*716^1-1
223*716^1-1
224*716^4-1
225*716^5-1
227*716^8-1
228*716^131-1
229*716^25-1
230*716^16-1
233*716^1972-1
234*716^1-1
237*716^1-1
[/code]Remaining k's: Tested to n=2500
[code]2*716^n-1
29*716^n-1
38*716^n-1
95*716^n-1
107*716^n-1
109*716^n-1
117*716^n-1
123*716^n-1
134*716^n-1
179*716^n-1
190*716^n-1
194*716^n-1
200*716^n-1[/code]Trivial Factor Eliminations:
[code]1
6
11
12
14
16
21
23
26
27
31
34
36
40
41
45
46
51
53
56
61
66
67
71
76
78
79
81
86
89
91
92
96
100
101
105
106
111
116
118
121
122
126
131
133
136
141
144
146
151
155
156
157
161
166
170
171
176
177
181
183
186
188
191
196
199
201
206
209
210
211
216
221
222
226
231
232
235
236[/code]Base Released

[quote=R. Gerbicz;198208]That would be a GFN prime for base=10, so it is very unlikely that there is a prime. (probably we know only: 10^(2^n)+1 is prime for n=0,1).[/quote]
So we'd need a prime 10^(2^x)+1 that can also be expressed as 10^(3*n+1)+1, right? For that to be, 2^x needs to be 1 mod 3, which means x needs to be even. I think it's safe to say Sierp base 1000 won't be proven by finding a prime in any of our lifetimes, if ever.

[QUOTE=Mini-Geek;198227]So we'd need a prime 10^(2^x)+1 that can also be expressed as 10^(3*n+1)+1, right? For that to be, 2^x needs to be 1 mod 3, which means x needs to be even. I think it's safe to say Sierp base 1000 won't be proven by finding a prime in any of our lifetimes, if ever.[/QUOTE]

We can also define Sierpinski/Riesel numbers in a way that we ignore all multipliers that give GFN numbers (my covering.exe used this definition). And in this case the conjecture is proven for this base.

[quote=R. Gerbicz;198234]We can also define Sierpinski/Riesel numbers in a way that we ignore all multipliers that give GFN numbers (my covering.exe used this definition). And in this case the conjecture is proven for this base.[/quote]
Oh okay, that makes sense. :smile: I wonder why the script has a section for k's eliminated because they're equivalent to GFNs, but didn't detect k=10 as such. Perhaps it only looks for GFNs in base b, so it didn't notice that k=10 made a base 10 GFN?

[quote=Mini-Geek;198236]Oh okay, that makes sense. :smile: I wonder why the script has a section for k's eliminated because they're equivalent to GFNs, but didn't detect k=10 as such. Perhaps it only looks for GFNs in base b, so it didn't notice that k=10 made a base 10 GFN?[/quote]

Now, isn't that interesting? Last night, when testing bases 512 and 1024, I discovered the same bug and believe-it-or-not, it is pretty rare. It only happens on even Sierp bases that are perfect powers where the k's that are the root of the base are not trivial.

That is there are more GFNs than just b^m*b^n+1. There's also q^m*b^n+1 where q is a perfect root of b (base). That is since 1000=10^3, then q=10, so k=10^0, 10^1, 10^2, etc. are also GFNs for base 1000.

I knew this from my experience with base 32, which has GFNs for k's that are powers of 2 (instead of only 32) and completely forgot about it when I made the final modifications to the script.

This shouldn't be hard to change the script. I need to add Willem as one of the main contributors in the comments anyway as well as put some sort of version in there. I'll call Karsten/Micha's original version 1.0, Willem's version 2.0, and Ian/my version 3.0. I'll then make the version with the correct for the GFNs version 3.1.


Gary

[quote=gd_barnes;198250]Now, isn't that interesting? Last night, when testing bases 512 and 1024, I discovered the same bug and believe-it-or-not, it is pretty rare. It only happens on even Sierp bases that are perfect powers where the k's that are the root of the base are not trivial.

That is there are more GFNs than just b^m*b^n+1. There's also q^m*b^n+1 where q is a perfect root of b (base). That is since 1000=10^3, then q=10, so k=10^0, 10^1, 10^2, etc. are also GFNs for base 1000.[/quote]
Hm...yeah, I see what you mean, and it does look pretty rare.
[quote=gd_barnes;198250]This shouldn't be hard to change the script.[/quote]
Ok good. :smile:

[quote=Mini-Geek;198259]Hm...yeah, I see what you mean, and it does look pretty rare.

Ok good. :smile:[/quote]

Just to clarify one more thing: Since k=1, 10, 100, etc. are GFN's for Sierp base 1000, as indicated by R. Gerbicz (Robert?), the base is proven.

I noticed that one thing that makes them more rare than expected is that many of the k's that make "non-standard" GFNs for bases are first eliminated by trivial factors and so would not get checked by the GFN routine. It is not possible for "standard" GFNs to be eliminated by trivial factors because standard GFN's can only have the factors of b and trivial k factors are based off of the factors of b-1. By mathematical rule, consecutive numbers cannot have any common factors. So they become an issue immediately and clearly if you don't eliminate them ahead of time and they don't have a prime at a fairly low n-value whereas the non-standard ones take a while to pop their heads up in somewhat unusual situations.

Edit: One more thing I just realized. I need to tweak my definition of GFN's on the web pages and the project definition in the "come join us" thread. Just another thing to do. lol


Gary

Reserving Riesel and Sierp bases 512 and 1024. (4 bases)

I've already run the script against all 4 to n=2500 but it has the GFN bug so I'm going to use them for testing when I get to that. Outstide of the erroneous GFNs remaining, there's not much remaining on most of them.

I've also wanted to kick start a few more power-of-2 bases. :smile:

Reserving the following bases (all new) to n=25K.

Reisel 729

Sierp 729

The above bases will all be complete in 4 days. I will report them 1 per day so Gary doesn't kill me.

Primes: (by b then k)
[code]2*509^1+1
2*524^1+1
3*524^2+1
2*539^7+1
2*554^1+1
3*554^1+1
2*569^29+1
2*584^111+1
3*584^1+1
2*599^13+1
2*614^1+1
3*614^18+1
2*629^1+1
2*644^1+1
3*644^1+1
2*659^1+1
2*674^5+1
3*674^3+1
2*689^3+1
2*704^1+1
3*704^1+1
2*719^1+1
2*734^3+1
3*734^1+1
2*749^1+1
2*764^1189+1
3*764^1+1
2*779^1+1
2*794^3+1
3*794^1+1
2*809^1+1
2*824^7+1
3*824^1+1
2*839^5+1
2*854^1+1
3*854^4+1
2*884^5+1
3*884^3+1
3*914^12+1
2*929^99+1
2*944^1+1
3*944^1+1
2*959^5+1
2*974^1+1
3*974^7+1
2*989^1+1
3*1004^19+1
2*1019^1+1
[/code]Sequences remaining:
[code]2*869^n+1
2*899^n+1
2*914^n+1
2*1004^n+1
[/code]GFN primes: (by b)
[code]554^4+1
584^2+1
614^256+1
644^2+1
674^2+1
704^2+1
764^2+1
824^1024+1
884^8+1
914^4+1
1004^2+1
[/code]GFNs with no primes to 32768 (2^15):
[code]524^n+1
734^n+1
794^n+1
854^n+1
944^n+1
974^n+1[/code]

Thanks Tim for the explanation on GFN's.

Are you testing the 4 k's left from your ck=4 post. If not, I have a PRPNET run going for n=2.5K-25K on a bunch of k's and I could add those to it.

They were:
2*869^n+1
2*899^n+1
2*914^n+1
2*1004^n+1

[quote=MyDogBuster;199130]Are you testing the 4 k's left from your ck=4 post. If not, I have a PRPNET run going for n=2.5K-25K on a bunch of k's and I could add those to it.

They were:
2*869^n+1
2*899^n+1
2*914^n+1
2*1004^n+1[/quote]
Nope I wasn't planning on working them, feel free to take those higher. Just be aware that taking such high bases to a large n value is rather slow. The tests grow large very quickly when you add 3 digits with each n! 1004^25K > 2^250K

Sierp
 

Proven with k=8:

primes:

2*1022^727+1
3*1022^1+1
4*1022^6+1
5*1022^5+1
6*1022^1+1
7*1022^36+1

Let me know if I'm missing anything.

reserving riesel base 589
it is currently at ~3k with 8 ks remaining
i will post details when i have taken it as far as i can

it seems riesel base 589 is a slightly interesting base
i have found interesting properties about two of the remaining ks

216*589^n-1
216 is 6^3
216*589^(3*n)-1=(6*589^n-1)*(36*589^(2*n)+6*589^n+1)
this should mean that i can remove all n that are 0 mod 3 for this k
does anyone have any hints on how to do this?

648*589^n-1
648 is 2^3*3^4
i dont think we can learn anything from this but someone may know better

edit:
i have already removed ks 144 and 324 because they are squares so even ns have algebraic factors and odd ns have a trivial factor of 5

[quote=henryzz;199317]216*589^n-1
216 is 6^3
216*589^(3*n)-1=(6*589^n-1)*(36*589^(2*n)+6*589^n+1)
this should mean that i can remove all n that are 0 mod 3 for this k[/quote]
Sounds right to me.
[quote=henryzz;199317]does anyone have any hints on how to do this?[/quote]
Here's what I'd probably do: load the sieved file into a spreadsheet program, add a column next to each one that is equal to n mod 3, sort by that column, delete all rows that are 0, and then resave it back with everything how it was. (OpenOffice.org Calc's Text to Columns and advanced settings for saving as a .csv would be very helpful here) Or you could make a Perl script to do it.

[quote=Mini-Geek;199324]Or you could make a Perl script to do it.[/quote]
Like this one: :smile:[code]#!/usr/bin/perl
#usage: file k a b
#e.g. 'mod 589 216 0 3' looks in 589.txt, removes values with k=216 and n=0 mod 3, and writes to 589-out.txt

open(IN, $ARGV[0].'.txt');
open(OUT, '>' .$ARGV[0].'-out.txt');
$k = $ARGV[1];
$a = $ARGV[2];
$b = $ARGV[3];
$removecount = 0;

while(<IN>)
{
$line = $_;
chomp($line);
@linearray = split(/ /,$line);
$thisk = @linearray[0];
#if this isn't the right k, then we don't want to remove it, so print it out
if ($thisk != $k) {
print OUT $line."\n";
next;
}
$thisn = @linearray[1];
#if there is nothing after a space on this line (usually the first line of a NewPGen-format file), then we don't want to remove it, so print it out
if ($thisn == '') {
print OUT $line."\n";
next;
}
$thisa = $thisn % $b;

#if the modular value isn't right, then we don't want to remove it, so print it out
if ($thisa != $a) {
print OUT $line."\n";
next;
}

#if we've got here, then everything matches, and we remove it by not doing anything, we also increment a counter so we can see how many were removed
$removecount++;
}
print "removed $removecount line(s)";

close(IN);
close(OUT);[/code]To use it, (say it's named mod.pl and the NewPGen-format file is 589.txt) run 'perl mod.pl 589 216 0 3', and it will write everything except k=216 values whose n=0 mod 3 to 589-out.txt. It's had only minimal testing, but I don't see any reason for it not to work as long as you use a NewPGen format file.

[quote=henryzz;199317]it seems riesel base 589 is a slightly interesting base
i have found interesting properties about two of the remaining ks

216*589^n-1
216 is 6^3
216*589^(3*n)-1=(6*589^n-1)*(36*589^(2*n)+6*589^n+1)
this should mean that i can remove all n that are 0 mod 3 for this k
does anyone have any hints on how to do this?

648*589^n-1
648 is 2^3*3^4
i dont think we can learn anything from this but someone may know better

edit:
i have already removed ks 144 and 324 because they are squares so even ns have algebraic factors and odd ns have a trivial factor of 5[/quote]


Ah, I see you happen to have chosen a tricky base. It's what keeps the conjectures interesting. The Sierp side is usually easier with few k's that have algebraic factors. Technically you don't need to worry about testing GFNs.

That is correct on removing n==(0 mod 3) for k=216.

To generalize your statements, for ANY k that is a perfect square on ANY base, you can remove n==(0 mod 2), that is even n's. For any k that is a perfect cube on any base, you can remove n==(0 mod 3). The same pattern applies to k's that are 5th powers, 7th powers, 11th powers, etc. for any prime power. Those are the k's that have algebraic factors to make a PARTIAL covering set for the k. If the other n's (i.e. odd n's on squared k's) can be eliminated by a "numerical" factor such as 3 or 5, that's when you have a k that has partial algebraic factors to make a FULL covering set, which is what you found with k=144 and 324.

As for your squared k's being removed, that is correct and see the algebraic factors thread. Any Riesel base that is b==(4 mod 5) will have SOME squared k's (not all) where even n's have algebraic factors and odd n's where there is a factor of 5. It's only the squared k's where k=m^2 and m==(2 or 3 mod 5). That is k=2^2, 3^2, 7^2, 8^2, 12^2, 13^2, 17^2, 18^2, etc. Your k=144 and 324 fit that criteria. You didn't encounter many of the others listed here because they were eliminated by a trivial factor.

As for k=648 remaining, you are correct. Nothing can be inferred from its factorization other than it is a very low weight k that should eventually have a prime. All odd n's have a factor of 59. The even n's have many small factors but not a covering set. The first n-value without a factor < 2000 is at n=22, which has a 21-digit smallest factor. So clearly no covering set there.

I also do exactly what Tim does on removing the even n's or the n's that are n==(0 mod 3). Personally, I don't worry about it for n<=10K. It's not worth my personal time. But above that, the CPU time savings is worth it.

(caps for emphasis)


Gary

[quote=Mini-Geek;199328]NewPGen format file.[/quote]
do u mean a .prp file as .npg files are only single k values?:smile:
might be worth editing that in in the script thread

I'm done with Riesel and Sierp bases 512 and 1024. These got a little tricky, especially on the Sierp side. There was both algebraic factors and unusual GFNs as well as testing from RPS and ProthSearch that helped eliminate some k's that I didn't. I only tested them to n=2500 but with testing from other projects, all of the remaining k's are at n>=145K. 2 are proven, one has 1 k remaining, and another has 2 k's remaining.

Particulars:

Riesel base 512 with a conjecture of k=14 is proven. Although cubed k's would have full algebraic factors, k=1 & 8 were already eliminated with a trivial factor of 7. This was the easy one.

Riesel base 1024 with a conjecture of k=81 has k=29 & 74 remaining. All squared k's have full algebraic factors, which eliminates k=9 & 36. After testing to n=2500, I had k=29, 39, & 74 remaining. For odd k's, base 2 Riesel primes convert to base 1024 Riesel primes if n==(0 mod 10). 39*2^40700-1 is prime, which converts to 39*1024^4070-1 so it is eliminated. For k=29, it has been tested to n=2M base 2 with no n==(0 mod 10) primes so it remains at n=200K base 1024. For k's==(2 mod 4), base 2 Riesel primes convert if n==(1 mod 10) where n>1. For k=74, it has been tested to n=1.45M base 2 with no n==(1 mod 10) n>1 primes so it remains at n=145K base 1024.

Sierp base 512 with a conjecture of k=18 has k=5 remaining and was the most unusual. Since 512=2^9, k=1, 2, 4, 8, & 16 are all GFN's. All cubed k's have full algebraic factors and in this case, it eliminates two of the GFN's, k=1 & 8, so we can't say that "k=1 and 8 are GFn's with no known prime" since it is mathematically impossible for them to have a prime. k=2, 4, & 16 have no known prime so are the only GFN's shown as such. As for k=5 remaining, the base 2 ProthSearch project has searched it to n=5.33M with no n==(0 mod 9) prime, which is the requirement for a base 512 prime. Hence k=5 remains at n=592.2K base 512. (I also updated the search limit for Sierp base 128 k=40.)

Sierp base 1024 with a conjecture of k=81 is proven and was a little unusual on its GFN elimination. Since 1024=2^10, k=1, 2, 4, 8, 16, 32, & 64 are all GFN's. k=2, 8 & 32 were eliminated by a trivial factor of 3. All k's that are perfect 5th powers have full algebraic factors, which eliminates k=1. k=64 has a prime at n=1; the only GFN on either of these bases with a known prime. This leaves only k=4 & 16 as GFN's with no known prime.

Bottom line:
Riesel base 1024 has the following remaining:
29 (200K)
74 (145K)

Sierp base 512 has the following remaining:
5 (592.2K)

I had hoped to open up some more power-of-2 bases testing but this didn't do it. What is remaining is being searched by RPS and ProthSearch. Like Sierp base 128, these aren't worth messing with.

The pages will shortly be updated for these bases.


Gary

Sierpinski base 605
 

Completed to n=20000 and released. k=70 remains. Here are the primes.

[code]
2*605^5+1
4*605^2+1
6*605^1+1
8*605^23+1
10*605^12394+1
12*605^5+1
14*605^3+1
16*605^2+1
18*605^1+1
20*605^1+1
22*605^4+1
24*605^3+1
26*605^1+1
28*605^2+1
30*605^34+1
32*605^13+1
34*605^2+1
36*605^5+1
38*605^3+1
40*605^86+1
42*605^1+1
44*605^11+1
46*605^2068+1
48*605^29+1
50*605^11+1
52*605^6+1
54*605^5+1
56*605^3+1
58*605^6+1
60*605^3+1
62*605^1+1
64*605^10+1
66*605^13+1
68*605^1+1
72*605^10+1
74*605^1+1
76*605^4+1
78*605^16+1
80*605^3+1
82*605^2+1
84*605^1+1
86*605^5+1
88*605^2+1
90*605^2+1
92*605^1+1
94*605^4+1
96*605^12+1
98*605^3+1
[/code]

[quote=henryzz;199367]do u mean a .prp file as .npg files are only single k values?:smile:
might be worth editing that in in the script thread[/quote]
By NewPGen I meant the format LLR uses, which in srfile is -G and writes to a .prp file. Although it would work just fine on anything that has "k n", (or even "k n c" or any other number of specifiers - as long as the first two are k and n, separated by spaces) such as .prp, (LLR/NewPGen) .npg, (single-k NewPGen) and ABC files, for single-k files there'd be the useless overhead of specifying and filtering the k.
Besides, I can't edit the other post myself, as it's way past the 1 hour mark, and I'm not a mod here.

Karsten reported:

50*601^30735-1 is prime

As far as I know, he has not reserved Riesel base 601.

[quote=gd_barnes;199435]Karsten reported:

50*601^30735-1 is prime

As far as I know, he has not reserved Riesel base 601.[/quote]
Actually,
BR601a.txt:120*601^4663-1 is 3-PRP! (4.1509s+0.0024s)
BR601a.txt:50*601^30735-1 is 3-PRP! (188.4408s+0.0183s)
BR601a.txt:624*601^44279-1 is 3-PRP! (564.9792s+0.0151s)

[COLOR=green]EDIT: The file is attached - it was running unattended and then interrupted at 45.36K and I will not continue anytime soon.[/COLOR]
[COLOR=green][/COLOR]
[COLOR=green]Overwhelmed by the deluge of new bases, I've stopped short of reporting those that I have reserved, but I'll try to organize and report them all now whereever they are stopped.[/COLOR]

[quote=Batalov;199436]Actually,
BR601a.txt:120*601^4663-1 is 3-PRP! (4.1509s+0.0024s)
BR601a.txt:50*601^30735-1 is 3-PRP! (188.4408s+0.0183s)
BR601a.txt:624*601^44279-1 is 3-PRP! (564.9792s+0.0151s)[/quote]

OK, I have Riesel base 601 as unreserved. The status is:

k=300, 482, and 744 still remain and the testing limit on them is n=2500.


Gary

[QUOTE=gd_barnes;199438]OK, I have Riesel base 601 as unreserved. The status is:

k=300, 482, and 744 still remain and the testing limit on them is n=2500.
[/QUOTE]

you should set the test-limit to 45.36k as Serge's file show.

so i will stop testing k=300!

OK, I will set the test limit on Riesel base 601 to n=45.36K on the remaining 3 k's. Since Serge states that he will not get back to it, I'll unreserve it.

Thanks for the results Serge. That helps a lot. :smile:


Gary

Sierp Base 729
 

Sierp Base 729
Conjectured k = 74
Covering Set = 5,73
Trivial Factors k == 1 mod 2(2) and 6 mod 7(7) and 12 mod 13(13)

Found Primes:
2*729^1+1
4*729^1+1
10*729^2+1
14*729^3+1
16*729^2+1
18*729^53+1
22*729^2+1
24*729^1+1
26*729^2+1
28*729^3+1
30*729^1+1
32*729^6+1
36*729^2+1
40*729^3+1
42*729^24+1
44*729^1+1
46*729^2+1
50*729^1+1
52*729^16+1
54*729^1+1
56*729^28+1
58*729^1+1
60*729^3+1
66*729^6+1
68*729^4+1
70*729^1+1
72*729^1+1

Remaining k's:
8*729^n+1 <------- Proven composite by full algebraic factors

Trivial Factor Eliminations: 8k's

Conjecture Proven

Sierp Bases 869, 899, 914 and 1004
 

Sierp Bases 869, 899, 914 and 1004 complete n=2.5K-25K

2*899^15731+1 is prime - Conjecture Proven

Bases Released - Results attached

Almost caught up on my new reservations so:

Reserving Riesel bases 529,676,784,900
to clean up some k's with full algebraic factors

Riesel Base 529
 

Riesel Base 529
Conjectured k = 54
Covering Set = 5, 53
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 11(11)

Found Primes: 15k's File attached

Remaining k's:
36*529^n-1 <----- Proven composite by full algebraic factors

Trivial Factor Eliminations: 10k's

Conjecture Proven

HTML attached

Riesel Base 676
 

Riesel Base 676
Conjectured k = 149
Covering Set = 7, 31, 37
Trivial Factors k == 1 mod 3(3) and k == 1 mod 5(5)

Found Primes: 76k's File attached

Remaining k's: Tested to n=25K
9*676^n-1 <----- Proven composite by full algebraic factors
144*676^n-1 <----- Proven composite by full algebraic factors

Trivial Factor Eliminations: 69k's


Conjecture Proven

HTML attached

Riesel Base 729
 

Riesel Base 729
Conjectured k = 74
Covering Set = 5,73
Trivial Factors k == 1 mod 2(2) and 1 mod 7(7) and 1 mod 13(13)

Found Primes: 25k's File attached

Remaining k's: Tested to n=25K
4*729^n-1 <----------- Removed due to full algebraic factors
16*729^n-1 <----------- Removed due to full algebraic factors
24*729^n-1

Trivial Factor Eliminations:
8
14
22
36
40
50
64
66

Base Released

HTML attached

Riesel Base 784
 

Riesel Base 784
Conjectured k = 156
Covering Set = 5, 157
Trivial Factors k == 1 mod 3(3) and k == 1 mod 29(29)

Found Primes: 93k's File attached

Remaining k's: Tested to n=25K
9*784^n-1 <----- Proven composite by full algebraic factors
36*784^n-1 <----- Proven composite by full algebraic factors
69*784^n-1
81*784^n-1 <----- Proven composite by full algebraic factors
116*784^n-1
144*784^n-1 <----- Proven composite by full algebraic factors

Trivial Factor Eliminations: 55k's

Base Released

HTML attached

Riesel Base 900
 

Riesel Base 900
Conjectured k = 52
Covering Set = 17, 53
Trivial Factors k == 1 mod 29(29) and k == 1 mod 31(31)

Found Primes: 41k's File attached

Remaining k's: Tested to n=25K
4*900^n-1 <----- Proven composite by full algebraic factors
9*900^n-1 <----- Proven composite by full algebraic factors
16*900^n-1 <----- Proven composite by full algebraic factors
22*900^n-1
25*900^n-1 <----- Proven composite by full algebraic factors
36*900^n-1 <----- Proven composite by full algebraic factors
49*900^n-1 <----- Proven composite by full algebraic factors

Trivial Factor Eliminations:
30
32

Base Released

HTML attached

i have had 2 more primes since n=3k
744*589^4026+-1
654*589^5638+-1
i am now tested upto n=20k
this lack of recent primes is getting frustrating

[quote=henryzz;200227]i have had 2 more primes since n=3k
744*589^4026+-1
654*589^5638+-1
i am now tested upto n=20k
this lack of recent primes is getting frustrating[/quote]

I don't blame you for being annoyed. If there's one thing I've personally found with the very large bases, it's that you can go into extremely long stretches of no primes after a large grouping of primes. I'm sure Ian can relate the same experience.

[QUOTE] I'm sure Ian can relate the same experience. [/QUOTE]

Yup, the galactic voids are all over the place. I guess this is part of the exercise. Not only can a pattern of primes be found (hopefully) but also a pattern of voids would also be useful.

[quote=gd_barnes;200281]I don't blame you for being annoyed. If there's one thing I've personally found with the very large bases, it's that you can go into extremely long stretches of no primes after a large grouping of primes. I'm sure Ian can relate the same experience.[/quote]
i worked out the probability using your odds or prime spreadsheet and i should have found 1.2 primes in the range 5k-10k and also 1.2 primes in the range 10k-20k
this was based on data after the primes just mentioned
i found the prime for 5k-10 before the analysis but am still owed the prime for 10k-20k
i suppose i was being lucky before
cant wait for finding another prime

Riesel base 707 proven with prime:

12*707^10572-1

No, I did not reserve it. I just took a bunch of bases that had a few k left where n < 25000 and are taking them to n = 25000 as part of my testing for the upcoming PRPNet release. I will avoid stepping on toes by not posting primes for bases reserved by others.

Riesel base 1019:

the only k=2 is at n=91k (so about n=910k for base 2)

no prime yet. continuing.

I found more primes during my PRPNet 3.0 testing.

109*716^4559-1
117*716^3831-1
123*716^11523-1
179*716^2898-1
2*716^4870-1
29*716^4054-1
194*716^6010-1

My apologies if I've stepped on any toes. AFAICT, these were released.

These bases are tested to 14000. I will continue with them (and a few others) to 25000.

[quote=rogue;200662]I found more primes during my PRPNet 3.0 testing.

109*716^4559-1
117*716^3831-1
123*716^11523-1
179*716^2898-1
2*716^4870-1
29*716^4054-1
194*716^6010-1

My apologies if I've stepped on any toes. AFAICT, these were released.

These bases are tested to 14000. I will continue with them (and a few others) to 25000.[/quote]

No problem. If you have a good idea of which bases you will be running to n=25K and can post them here, I'll go ahead and reserve them for you to avoid any duplication of work.


Gary

[quote=gd_barnes;200767]No problem. If you have a good idea of which bases you will be running to n=25K and can post them here, I'll go ahead and reserve them for you to avoid any duplication of work.

Gary[/quote]

Riesel bases 589, 716

Sierpinski bases 605, 781, 811, 961

[quote=rogue;200899]I was PM'd about it, so I discontinued searching it.[/quote]

OK, I have another one: Henryzz has Riesel base 589 reserved and already searched to n=20K.

[quote=rogue;200769]Riesel bases 589, 716

Sierpinski bases 605, 781, 811, 961[/quote]

These are all searched to 25K. Here are the primes:

107*716^17014-1

816*589^22557-1

I am reserving Riesel and Sierpinski bases 516, 520, 803, and 928.

[quote=rogue;201400]These are all searched to 25K. Here are the primes:

816*589^22557-1

I am reserving Riesel and Sierpinski bases 516, 520, 803, and 928.[/quote]
unreserving riesel 589 then
once i have finished sieving my sieve file from 25k-100k to 2T i will post a sieve file
i am at about 1.3T now

[QUOTE=henryzz;201418]unreserving riesel 589 then
once i have finished sieving my sieve file from 25k-100k to 2T i will post a sieve file
i am at about 1.3T now[/QUOTE]

Sorry about that. I missed your reservation.

[quote=rogue;201400]These are all searched to 25K. Here are the primes:

816*589^22557-1

I am reserving Riesel and Sierpinski bases 516, 520, 803, and 928.[/quote]

David, Mark's intent was to only search the above to n=25K. Therefore, if you'd like you can leave R589 reserved on up to n=100K. For now, that is how I'll show it on the reservations page.


Gary

Mark,

Did you read post 858? If not, here is a link:

[URL]http://www.mersenneforum.org/showpost.php?p=200902&postcount=858[/URL]

This was an important post about others reservations (the 2nd time that R589 was shown as reserved).

I followed up and said henryzz had R589 to n=25K. This after the people had previously posted that they had them reserved and they were shown as reserved on the web pages.

In total, you reserved 5 bases already reserved by others and have searched other's ranges on 2 of them. The 2 above, 1 by Willem that you were PM'd about, and 2 by Batalov that I chose to ignore because they apparently have been abandoned and have holes in the search ranges.

Please pay attention to reservations in the future. The web pages are almost always up to date to 2-3 days ago and it's simple enough to look through 2-3 days worth of postings here for further confirmation.


Thank you,
Gary