Riesel/Sierp #'s for bases 3, 7, and 15
 

Hidiho,

I've done some programming this week and this is what I found:

Base 7 cover set = 5, 13, 19, 43, 73, 181, 193, 1201
Smallest Riesel = 408034255082

Base 15 cover set = 13, 17, 113, 211, 241, 1489, 3877
Smallest Riesel = 36370321851498

I'll be tinkering a bit more with my code and then I'll show it here on the forum.

Laters, Willem.

[quote=Siemelink;133704]Hidiho,

I've done some programming this week and this is what I found:

Base 7 cover set = 5, 13, 19, 43, 73, 181, 193, 1201
Smallest Riesel = 408034255082

Base 15 cover set = 13, 17, 113, 211, 241, 1489, 3877
Smallest Riesel = 36370321851498

I'll be tinkering a bit more with my code and then I'll show it here on the forum.

Laters, Willem.[/quote]

If you are correct, this is HUGE, especially for base 7 where the conjecture dropped substantially! I'll do some verification myself and if they are correct, I will change the web pages.

Can you do the same thing for the Sierp side on both bases?


Gary

I've now confirmed these to be correct, although cannot guarantee that they are the lowest Riesel values. Proofs:

408034255082*7^n-1:
[code]
Factor n-occurrences n-remaining
19 n==(1 mod 3) n==(0,2 mod 3)
5 n==(3 mod 4) n==(0,2,5,6,8,9 mod 12)
43 n==(2 mod 6) n==(0,5,6,9 mod 12)
1201 n==(1 mod 8) n==(0,5,6,12,18,21 mod 24)
13 n==(6 mod 12) n==(0,5,12,21 mod 24)
181 n==(0 mod 12) n==(5,21 mod 24)
73 n==(5 mod 24) n==(21 mod 24)
193 n==(21 mod 24) (none)
[/code]

36370321851498*15^n-1:
[code]
Factor n-occurrences n-remaining
241 n==(1 mod 3) n==(0,2 mod 3)
113 n==(2 mod 4) n==(0,3,5,8,9,11 mod 12)
211 n==(3 mod 6) n==(0,5,8,11 mod 12)
17 n==(4 mod 8) n==(0,5,8,11,17,23 mod 24)
1489 n==(0 mod 8) n==(5,11 mod 12)
13 n==(5 mod 12) n==(11 mod 12)
3877 n==(11 mod 12) (none)
[/code]

A nice piece of programming Willem! :smile:

The Riesel conjecture web pages have now been updated.


Gary

They are the lowest for this cover set.
There may be different cover sets that repeat every 24n. But those also do not give a lower riesel.

I will check a bit deeper (36n or 48n) but my program isn't ready for that yet.
I need to improve on the efficiency before I can tackle base 3. The proposed cover set for that one repeats every 144n.

Laters, Willem.

Good work Siemelink. The real challenge is in base 3, where I would like to think there is a really much lower Sierpinski and Riesel.

Wow! That is really great work. Having studied these ideas in the past, I always appreciate seeing someone find lower Riesel and Sierpinski k's and the corresponding covering sets.

Congrats.

P.S. You may be able to "brute force" the base 7 result now. This can be done with looping in NewPGen and/or pfgw, I believe.

[QUOTE=gd_barnes;133739]I've now confirmed these to be correct, although cannot guarantee that they are the lowest Riesel values.[/QUOTE]

1*7^n-1 is also composite for every positive n, so k=1 would be the smallest Riesel value, or what are you searching? If you accept only even k values, then 4*7^n-1 is also composite for every positive n, because it's >3 and divisible by 3.

[quote=R. Gerbicz;133765]1*7^n-1 is also composite for every positive n, so k=1 would be the smallest Riesel value, or what are you searching? If you accept only even k values, then 4*7^n-1 is also composite for every positive n, because it's >3 and divisible by 3.[/quote]

k=1 and k=4 have trivial factors of 3 for all n-values and hence are not considered. For Riesel base 7, we do not consider k==(1 mod 3) where all n-values have a trivial factor of 3 nor k==(1 mod 2) where all n-values have a trivial factor of 2.

Therefore for Riesel base 7, we only consider k==(0 mod 6) and k==(2 mod 6). Taking it further, for Sierp base 7, we would only consider k==(0 mod 6) and k==(4 mod 6).


Gary

Tada!
 

Smallest Riesel for base 3 = 1910197852104712
Cover set = {5, 7, 13, 17, 41, 73, 97, 193, 577, 6481}
With factor in sequence length 48:
5 6481 13 7 5 13 41 73 13 7 17 13 5 97 13 7 5 13 193 73 13 7 41 13 5 6481 13 7 5 13 41 73 13 7 193 13 5 577 13 7 5 13 17 73 13 7 41 13

Spoke too soon!
 

Smallest Riesel for base 3 = 1200424637252
Cover set = {5, 7, 13, 19, 37, 41, 73, 757, 6481}
With factor in sequence length 72:
13 19 6481 13 5 7 13 37 5 13 73 7 13 757 41 13 5 7 13 19 5 13 41 7 13 37 6481 13 5 7 13 757 5 13 73 7 13 19 41 13 5 7 13 37 5 13 41 7 13 757 6481 13 5 7 13 19 5 13 757 7 13 37 41 13 5 7 13 757 5 13 41 7

Riesel base 3
 

The notation is slightly different on the linked webpage, but the point is that

2*31532322469*3^n-1 is always composite.


[url]http://tech.groups.yahoo.com/group/primeform/message/4698[/url]

Once again, nice work Willem. It's unfortunate that we weren't aware of this 11-digit Riesel value for base 3 that was discovered in 2004!

So unofficially, the Riesel value for base 3 is now 63,064,644,938. I will do my checking like I did before and if it looks good, I'll change the web page.

Assuming it is correct, this now makes the Riesel base 3 conjecture potentially proveable in our lifetimes now! :smile:

Masser, if you know of any more obscure web pages, discussion threads, etc. that have lower Riesel/Sierpinski numbers for bases 3, 7, or 15 then are currently shown on our web pages here, let us know.


Thanks,
Gary

This cover set {5,7,13,17,19,37,41,193,757} produces Riesels with a sequence length 144 (I think). My program has checked all the values under that. It needs another efficiency gain before I can run that length quickly.
Or, if I cap the primes at 758 I can find the smallest Riesel for this cover set.

Having fun, Willem.

You might also put your program to work to look at Sierpinski base 3, where a lot of work has been done, but you might be able to do better than the mooted k
3574321403229074.

also other Sierpinskis
base 7, k value 162643669672445
base 15, 91218919470156
base 71, 5917678826

Chris Caldwell would be interested in your results if you beat these.

Also there is a real challenge to see if you can use partial covering sets created by algebra, as x^n+1 often factors algebraically. This is especially relevent to x^3+1 which should provide algebraic factors, but I have been stumped in my efforts to make this work.

[quote=robert44444uk;133966]You might also put your program to work to look at Sierpinski base 3, where a lot of work has been done, but you might be able to do better than the mooted k
3574321403229074.

also other Sierpinskis
base 7, k value 162643669672445
base 15, 91218919470156
base 71, 5917678826

Chris Caldwell would be interested in your results if you beat these

Also there is a real challenge to see if you can use partial covering sets created by algebra, as x^n+1 often factors algebraically. This is especially relevent to x^3+1 which should provide algebraic factors, but I have been stumped in my efforts to make this work.[/quote]


We already have these as the Sierp numbers as shown on the web pages with the exception of base 71 that we are not working on.

On algebraic factors, the Riesel side generally has many more of them as k^(2q)-1 factors to (k^q-1)*(k^q+1) for all even n so that odd n only needs a trivial factor -or- (m^2)^(q^2)-1 factors to (m^q-1)*(m^q+1) for all n. For a most unusual example, see the discussion in the "algebraic factors issues for base 24" thread.

We do not consider any Riesel or Sierp value to be one that contains algebraic factors to make a full covering set so finding a k-value that fits that criteria does not lower the conjecture from the project's perspective. Otherwise on the Riesel side, the "conjectures" would be very low and uninteresting and mostly proven, i.e. Riesel base 9 would be k=4, Riesel base 12 would be k=25, Riesel base 16 would be k=9, etc.

I think if Prof. Caldwell takes a look at the Riesel side, he will conclude the same thing. I had responded to the paper that he sent me not long after the project was started suggesting this.

For that reason, our Sierp base 16 conjecture differs from Prof. Caldwell's paper. We consider it to be k=66741 with 28 k's remaining after a search to n=132K whereas his paper considers the "conjecture" to be proven at k=2500, which has algebraic factors to make a full covering set as shown on our powers-of-2 web page. k=40000 also has a similar condition.

That said, it is a good thing to find k-values with algebraic factors that make a full covering set so that we can eliminate them from our testing. Riesel base 24 turned out to be quite the challenge in that regard as did Riesel base 12, the latter of which is now proven and BOTH of which have 2 different sets of algebraic factors that make full covering sets to eliminate various k-values. BTW, Riesel base 24 would have a proven "conjecture" of k=6 if we chose to include algebraic factors making a full covering set as the Riesel number, which of course would be most 'boring'. :smile:

We do know this for Sierp base 3: We have found primes for ALL even k<2930054!! So if there are any algebraic factors for the base, they are rare indeed! It seems unlikely at this point but you never really know and always have to be on the lookout for them.


Gary

[quote=gd_barnes;133943]Once again, nice work Willem. It's unfortunate that we weren't aware of this 11-digit Riesel value for base 3 that was discovered in 2004!

So unofficially, the Riesel value for base 3 is now 63,064,644,938. I will do my checking like I did before and if it looks good, I'll change the web page.

Assuming it is correct, this now makes the Riesel base 3 conjecture potentially proveable in our lifetimes now! :smile:

Masser, if you know of any more obscure web pages, discussion threads, etc. that have lower Riesel/Sierpinski numbers for bases 3, 7, or 15 then are currently shown on our web pages here, let us know.


Thanks,
Gary[/quote]

[quote=Siemelink;133952]This cover set {5,7,13,17,19,37,41,193,757} produces Riesels with a sequence length 144 (I think). My program has checked all the values under that. It needs another efficiency gain before I can run that length quickly.
Or, if I cap the primes at 758 I can find the smallest Riesel for this cover set.

Having fun, Willem.[/quote]


I agree with this. The new Riesel base 3 value for the project is now 63064644938. Proof:

[code]
Factor n-occurrences n-remaining
13 n==(1 mod 3) n==(0,2 mod 3)
5 n==(3 mod 4) n==(0,2,5,6,8,9 mod 12)
7 n==(0 mod 6) n==(2,5,8,9 mod 12)
41 n==(5 mod 8) n==(2,8,9,14,17,20 mod 24)
757 n==(2 mod 9) n==(8,9,14,17,26,32,33,41,44,50,57,62,68 mod 72)
17 n==(1 mod 16) n==(8,9,14,26,32,41,44,50,57,62,68,80,86,89,98,104,105,116,122,134,140 mod 144)
193 n==(9 mod 16) n==(8,14,26,32,44,50,62,68,80,86,98,104,116,122,134,140 mod 144)
19 n==(8 mod 18) n==(14,32,50,68,86,104,122,140 mod 144)
37 n==(14 mod 18) (none)
[/code]

The web page will be updated shortly. I think KEP will be happy to hear this! :smile:

I renamed the thread to include base 3.


Gary

I can now test base 3 with a speed of about 1M k's per hour, upto n=1000

Testing higher takes 'too much' time.

But this means that, with the mooted riesel conjecture of k=63,064,644,938
we need about 63000 hours worth of testing them ALL to 1k.

Which is about 2625 days, which is 'only' about 7-8 CPU years.

Testing 10M candidates resulted in a handy 2150 remaining,
so in the end: 6306*2150 = about 14M candidates remaining.

[quote=michaf;133990]I can now test base 3 with a speed of about 1M k's per hour, upto n=1000

Testing higher takes 'too much' time.

But this means that, with the mooted riesel conjecture of k=63,064,644,938
we need about 63000 hours worth of testing them ALL to 1k.

Which is about 2625 days, which is 'only' about 7-8 CPU years.

Testing 10M candidates resulted in a handy 2150 remaining,
so in the end: 6306*2150 = about 14M candidates remaining.[/quote]


OK, fire away but be sure and coordinate with KEP on this reservation and let me know what k-range you will take. (I'm assuming you won't be taking all of them...yet, anyway, lol.) You'll have quite a bit of manual intervention with so many k's remaining but with a much lower conjecture, I suppose it won't be too bad.


Gary

[QUOTE=gd_barnes;133993]OK, fire away but be sure and coordinate with KEP on this reservation and let me know what k-range you will take. (I'm assuming you won't be taking all of them...yet, anyway, lol.) You'll have quite a bit of manual intervention with so many k's remaining but with a much lower conjecture, I suppose it won't be too bad.

Gary[/QUOTE]

The manual intervention is indeed too much when dealing with such huge number of numbers...

Does anyone know of the existance of a program to delete all lines which are in one file, from another file?
Or is anyone skilled in perl to do so with a quick few commands?

edit: I also tried testing at once upto 10k, which leads to 1.5M done in about 5 hours, leaving some 30 candidates

[QUOTE=gd_barnes;133993]OK, fire away but be sure and coordinate with KEP on this reservation and let me know what k-range you will take. (I'm assuming you won't be taking all of them...yet, anyway, lol.) You'll have quite a bit of manual intervention with so many k's remaining but with a much lower conjecture, I suppose it won't be too bad.

Gary[/QUOTE]

Which k's were tested above 100M? I know only of my own 100-110M

[quote=michaf;134026]The manual intervention is indeed too much when dealing with such huge number of numbers...

Does anyone know of the existance of a program to delete all lines which are in one file, from another file?
Or is anyone skilled in perl to do so with a quick few commands?

edit: I also tried testing at once upto 10k, which leads to 1.5M done in about 5 hours, leaving some 30 candidates[/quote]
Actually, I have just recently been working on a Perl script to do just that for KEP. I've got it working fine on Linux already; I still have yet to make the necessary modifications for it to run on Windows, and then compile it into a .exe file.

If you'd like me to send you the finished Linux version, just PM me your email address. When I get the Windows version finished, too, I'll post both here on the forum. :smile:

[QUOTE=Anonymous;134034]Actually, I have just recently been working on a Perl script to do just that for KEP. I've got it working fine on Linux already; I still have yet to make the necessary modifications for it to run on Windows, and then compile it into a .exe file.

If you'd like me to send you the finished Linux version, just PM me your email address. When I get the Windows version finished, too, I'll post both here on the forum. :smile:[/QUOTE]

Just the .pl script would be fine, I can run it here (or at least I think I can)

[quote=michaf;134038]Just the .pl script would be fine, I can run it here (or at least I think I can)[/quote]
Okay, just a little warning though: there are a lot of Linux-specific commands hardcoded into it, so you'll have to modify those if you want to run it on Windows.

(Got your PM, will send you the script shortly...)

I think it is great that base 3 might be capable of attack with brute force!!!! This would be an important challenge. I would be interesting in joining in the fun for n<1000 if an automated windows executable is developed.

[quote=michaf;134031]Which k's were tested above 100M? I know only of my own 100-110M[/quote]

Micha,

We're talking the Riesel side here. Check out the thread above where the 11-digit k-value is the RIESEL # and where you stated it would take 6300 runs of 10M k-values each. Your k=100M-110M was for the Sierp side. The Sierp conjecture has not changed. (As I've said before...too many bases floating around!) :smile:

Only KEP has worked on the Riesel side and his last status had him at k=2M and he had reserved up to k=10M. I think he plans to continue up to k=10M so you could do Riesels for anything k>10M.

I'm the only one working on the Sierp side now. My last status had me at k=15M but I'm now almost up to k=25M and n=25K. I'll post a status and the additional k's remaining when I get there. Of course then you did k=100M-110M and KEP did k=110M-120M.

If you work on the Sierp side, the gap of k=30M-100M should be filled in first. (My reservation now goes to k=30M.) Otherwise, as KEP found out for k=110M-120M, it gets very confusing determining the k's remaining because they need to be reduced as much as possible and then compared to lower k's that are already remaining, which usually eliminates some of them.

When I get a chance, I'll 'process' your k=100M-110M k-values remaining and get them listed on the web pages. I imagine that at least a few of them will reduce to k-values already remaining and hence can be eliminated. Others will be able to be reduced (i.e. divided by 3 or 9) but will still be remaining. (The 37M-40M k-values that you see currently remaining are reduced from KEP's k=110M-120M work.)

The web pages contain up-to-date reservation and completion info. for both Riesel and Sierp base 3 with the exception of your completion of the sierp k=100M-110M range.


Gary

[quote=robert44444uk;134054]I think it is great that base 3 might be capable of attack with brute force!!!! This would be an important challenge. I would be interesting in joining in the fun for n<1000 if an automated windows executable is developed.[/quote]

Just remember, we're talking only the Riesel base 3 conjecture that has been reduced and hence capable of a brute force attack.

I've actually already worked the 10M-100M k range up to n=5,000. But as soon as Anon sends me his program, I would really like to work on the entire Riesel Base 3 by myself, untill at least n=25,000. Not to be selffish, but to avoid spending precious cycles on doubleling each others efforts. So for evryone for the future [B]Please ask me or at least check out my website before working on the Riesel Base 3[/B], because it seems to be getting bit of a bad habbit that people doubles each others work and ressources is wasted :(

KEP!

The Sierpinski side should be reducable using the same covering set. I am sure Willem can work that out.

[QUOTE=masser;134101]The Sierpinski side should be reducable using the same covering set. I am sure Willem can work that out.[/QUOTE]

For the moment I am concentrating on the Riesels. Once I have the program in a satisfactory state I'll port it to do Sierpinski's as well.

Yesterday I ran my program while limiting the primes to 1000 or lower. This gave me the same answer as the one that we have now. When I use 1 more prime, 6831, my program gets so slow that it isn't worth to wait for the answer. There is one area that is clearly inefficient, but I have to think a bit before I know how to get it better.

Willem.

I'll be darned...

Sierp it was indeed for 100-110M...

and KEP, if you want it, it's all yours...
I'll send you a small pfgw script if you like,
that was what I was using when I got to 1M/hour (to n=1k)

it just goes from n=1 to n=1000, factoring with standard pfgw-setting, and testing if prime; when a prime found, skip to next k.

[QUOTE=michaf;134151]I'll be darned...

Sierp it was indeed for 100-110M...

and KEP, if you want it, it's all yours...
I'll send you a small pfgw script if you like,
that was what I was using when I got to 1M/hour (to n=1k)

it just goes from n=1 to n=1000, factoring with standard pfgw-setting, and testing if prime; when a prime found, skip to next k.[/QUOTE]

I actually wasn't sure that I would really like to continue... but maybe you can send me in PM the script, then I shure may consider give it a try and continue attacking this major (yet very reduced challenge). However I don't get it, if nothing is differint from regular WinPFGW why is it faster and how about remaining k's, is there any easy way to recover those remaining without to much hassel when doing a single k up to n=1000?

KEP!

@Michaf:

It appears that you have the energy to carry out the Base 3 Riesel search, so would you like to take over the entire range, from k=>100M and complete these to n=25,000? I think it would be more fair for letting people who is more frequently around on the site (in stead of once a week, like me) to run these kind of challenges :smile: Also I seem to have had a hard time recovering from my latest illness, so for the time being I think I'll finish the ranges for Base 3 Riesel with n<=25,000 as mentioned here, and finish bringing Base 19 Sierpinski up to n<=100,000.

By the way: Thanks for taking interest in doing this Base 3 search, and thanks to our Hungarian user for bringing this down more than a million times. Now I actually think if the other big conjectures, both sierpinski and riesel, can be reduced, and we at somepoint can have a BOINC workframe or something like that, that we might actually be able to reach into the hundreds of bases before man returns to the moon or sets foot on Mars, anyone reading it as a challenge?

Take care!

KEP

[QUOTE=KEP;134165]@Michaf:

It appears that you have the energy to carry out the Base 3 Riesel search, so would you like to take over the entire range, from k=>100M and complete these to n=25,000? I think it would be more fair for letting people who is more frequently around on the site (in stead of once a week, like me) to run these kind of challenges :smile: Also I seem to have had a hard time recovering from my latest illness, so for the time being I think I'll finish the ranges for Base 3 Riesel with n<=25,000 as mentioned here, and finish bringing Base 19 Sierpinski up to n<=100,000.

By the way: Thanks for taking interest in doing this Base 3 search, and thanks to our Hungarian user for bringing this down more than a million times. Now I actually think if the other big conjectures, both sierpinski and riesel, can be reduced, and we at somepoint can have a BOINC workframe or something like that, that we might actually be able to reach into the hundreds of bases before man returns to the moon or sets foot on Mars, anyone reading it as a challenge?

Take care!

KEP[/QUOTE]

Thanks, KEP,

I don't have the computerpower to run 8 cpu-years, unfortunately :(
this test was on a laptop, so maybe a 'normal' computer will be quicker.
The perfect thing about the script is, that it works sequential, so you can just start off where you left; a power-outage will now result in much less work to restart.

The script will output one file: it contains just the k's which have no primes upto 1k.

When I get the time, I'll try to write a script that takes it on from 1k onward on a more convenient non-intervening way (My script-writing skills need a LOT of honing, so I need the challenge :) )

Does anyone know what the maximum number of sequences is for srsieve?
This would largely determine the need for manual intervention...

KEP, I'll PM you the script in a sec

[QUOTE=michaf;134170]Thanks, KEP,

I don't have the computerpower to run 8 cpu-years, unfortunately :(
this test was on a laptop, so maybe a 'normal' computer will be quicker.
The perfect thing about the script is, that it works sequential, so you can just start off where you left; a power-outage will now result in much less work to restart.

The script will output one file: it contains just the k's which have no primes upto 1k.

When I get the time, I'll try to write a script that takes it on from 1k onward on a more convenient non-intervening way (My script-writing skills need a LOT of honing, so I need the challenge :) )

Does anyone know what the maximum number of sequences is for srsieve?
This would largely determine the need for manual intervention...

KEP, I'll PM you the script in a sec[/QUOTE]

OK I got your script. I'll try to make it work, but how do I run it using WinPFGW? Also will it be possible to ask the range to end at some point? Like every billion or 15 billion k's (which means my Quad can do a quarter each core)?

About srsieve, according to reply from Geoff, the amount of candidates for Base 3 is limited to memory issues only, so if one has enough memory, it shouldnt be a big issue to use srsieve :smile:

Regards

Kenneth!

Ps. Actually if I makes your script work, I would really like to throw in the effort and try to break this challenge up to at least n=25,000. However we all has to remember that WinPFGW (without sieving) gets hopelessly ineffecient above n=1,000 or with a little luck above n=2,500.

[QUOTE=KEP;134187]OK I got your script. I'll try to make it work, but how do I run it using WinPFGW? Also will it be possible to ask the range to end at some point? Like every billion or 15 billion k's (which means my Quad can do a quarter each core)?[/QUOTE]

Would someone mind posting the script here? I would like to take a look at it.

[QUOTE=rogue;134208]Would someone mind posting the script here? I would like to take a look at it.[/QUOTE]

I guess someone can delete this post, if Michaf is against me publicing the script that he wrote and I am going to use :smile: :

--------------------------------------------------------------------------
SCRIPT // autobodgified by scriptify.pl
: pre-declare scriptify's globals
DIMS PCtmpString
DIMS str
OPENFILEAPP logfile,log.out
DIM k,2
DIM n,1
DIM primefound
DIM bignum,k*3^n-1
PRP bignum
SET k,100000000
SET n,1
LABEL label
SET bignum,k*3^n-1
PRP bignum
IF !(ISPRIME) THEN GOTO PCnotif_a
SET k,k+(2)
PRINT k
SET n,1
GOTO label
GOTO PCendelse_b
LABEL PCnotif_a
IF !(n<1000) THEN GOTO PCnotif_c
SET n,n+(1)
GOTO label
GOTO PCendelse_d
LABEL PCnotif_c
: synthesise fprintf
SETS PCtmpString,%d;k
WRITE logfile,PCtmpString
SET n,1
SET k,k+(2)
GOTO label
LABEL PCendelse_d

LABEL PCendelse_b

END
--------------------------------------------------------------------------

Actually Michaf did send me another one, which lies in my PM, but the above one, is workable if you copy it into a notepad and names it "*.pl", and then ask WinPFGW to run it. However the script has some lackings, since it appears that there is no way it saves the PRP or at least verifys it as a composite or a strict prime, before moving on to next k. Also its impossible to see in the pfgw.log and pfgw-prime.log file what k/n pair is primed, hence this makes it virtually impossible to compare the verification file once one verifys the PRP and of course when running billions a few PRP will fail to be primes, and then you really has no chance, to know which k is not in fact a prime and therefor still remaining. I've written this to Michaf, and is expecting to hear from him sometimes, because there were a list of things I would like to be able to do before switching to use only that script (even though it is a lot faster, 100M k's on a Quad core a day). But hey let's wait and see what he says when he gets out of bed and sneaks up to his computer (hope it doesn't get scared once it realise Michaf is in front of it) :smile:

Take care!

Kenneth!

[QUOTE=KEP;134215]
SCRIPT // autobodgified by scriptify.pl
: pre-declare scriptify's globals
DIMS PCtmpString
DIMS str
OPENFILEAPP logfile,log.out
DIM k,2
DIM n,1
DIM primefound
DIM bignum,k*3^n-1
PRP bignum
SET k,100000000
SET n,1
LABEL label
SET bignum,k*3^n-1
PRP bignum
IF !(ISPRIME) THEN GOTO PCnotif_a
SET k,k+(2)
PRINT k
SET n,1
GOTO label
GOTO PCendelse_b
LABEL PCnotif_a
IF !(n<1000) THEN GOTO PCnotif_c
SET n,n+(1)
GOTO label
GOTO PCendelse_d
LABEL PCnotif_c
: synthesise fprintf
SETS PCtmpString,%d;k
WRITE logfile,PCtmpString
SET n,1
SET k,k+(2)
GOTO label
LABEL PCendelse_d
LABEL PCendelse_b
END[/QUOTE]

It should be possible to use srsieve to kick out a pre-sieved file (across many k and n), then use a script similar to this to PRP test the inputs and skip to the next k when a prime is found for a given k/n combination. You can change the WRITE command to write bignum instead of PCtmpString and that will log the PRP, not just the value of k. With a small change to srsieve, I think you can have it sieve a thousand or so k at a time and append to an output file that could then be read by the script after a few million k have been sieved.

BTW, does someone have a list of all primes for the k that have been removed? It must be a fairly large file.

[QUOTE=KEP;134187]OK I got your script. I'll try to make it work, but how do I run it using WinPFGW? Also will it be possible to ask the range to end at some point? Like every billion or 15 billion k's (which means my Quad can do a quarter each core)?

About srsieve, according to reply from Geoff, the amount of candidates for Base 3 is limited to memory issues only, so if one has enough memory, it shouldnt be a big issue to use srsieve :smile:

Regards

Kenneth!

Ps. Actually if I makes your script work, I would really like to throw in the effort and try to break this challenge up to at least n=25,000. However we all has to remember that WinPFGW (without sieving) gets hopelessly ineffecient above n=1,000 or with a little luck above n=2,500.[/QUOTE]

In part, see your PM's.
To run in WinPFGW, just use: 'riesel3.scr -f' in the input window.
(-f factors it to the 'standard' depth in winpfgw)

On srsieve: that would be wonderful :)

On winpfgw: I've tested 0.3M per hour when testing to 10k
and 1M per hour to 1k,
and 2M per DAY ro 25k!

I think testing to 10k is worth the effort of tripling the initial time.

I haven't tested to 5k.

Rogue, the original script is:
[CODE]string str;
file logfile=fopen("log.out", "a");
integer k=2;
integer n=1;
integer primefound=0;
integer bignum=k*3^n-1;
PRP(bignum);

k=30000000;
n=1;

label :

bignum=k*3^n-1;
PRP(bignum);
if(ISPRIME) {
k+=2;
print(k);
n=1;
goto label;
} else {
if(n<25000) {
n+=1;
goto label;
} else {
fprintf(logfile, "%d", k);
n=1;
k+=2;
goto label;
}
}
[/CODE]

I can send you the scriptify - thingy which makes this into a working pfgw-script too,if you don't have it.

Oh, and no, I don't mind the script to bepublished at all :)
Just do not bash on it too hard, I know it can be improved in thousands of ways :)

On my Quad core, I can bring down 600000 k's. each hour if going to only n<=1k :smile:.

For SrSieve, sieving 1541 base 19 candidates for sierpinski took around 12 Mb of RAM, so I think sieving thousands upon thousands of candidates should be rather easy. And again, I'm not interested in finding PRP only primes, but I may asses what you have suggested Rogue, and see if this can work.

Oh and about storering the k/n prime list for k<=100M, it is about 800Mb uncompressed and compressed around 100Mb :smile:

Hope I got it all, take care my hard working friends :smile:

Kenneth!

[QUOTE=KEP;134267]On my Quad core, I can bring down 600000 k's. each hour if going to only n<=1k :smile:.

For SrSieve, sieving 1541 base 19 candidates for sierpinski took around 12 Mb of RAM, so I think sieving thousands upon thousands of candidates should be rather easy. And again, I'm not interested in finding PRP only primes, but I may asses what you have suggested Rogue, and see if this can work.

Oh and about storering the k/n prime list for k<=100M, it is about 800Mb uncompressed and compressed around 100Mb :smile:

Hope I got it all, take care my hard working friends :smile:

Kenneth![/QUOTE]

Do you use -f in pfgw? It sounds like you are prp-ing ALL values, while you better can try to factor it first.

Rogue, the script is a bit updated:

version 0.2 now:

It saves primes found in primes.out
It saves NO primes sequences in NOprimes.out
It has a starting and stopping value for n and k
It writes the sequence instead of just k
(123456*3^n-1) instead of 123456


[CODE]file noprimesfile=fopen("NOprimes.out", "a");
file primefile=fopen("primes.out", "a");
integer mink=30000000;
integer maxk=30000500;
integer minn=1;
integer maxn=100;
integer bignum;
integer k;
integer n;

k=mink;
n=minn;

label :

if(k>maxk) {
goto end;
}

bignum=k*3^n-1;
PRP(bignum);
if(ISPRIME) {
fprintf(primefile, "%d*3^%d-1", k, n);
k+=2;
print(k);
n=1;
goto label;
} else {
if(n<maxn) {
n+=1;
goto label;
} else {
fprintf(noprimesfile, "%d*3^n-1", k);
n=1;
k+=2;
goto label;
}
}

end :[/CODE]

@Michaf: I was doing PRP testing of all values untill now. However I still have the problem, when asking following: script.pl -f -tp, it runs 20002 tests and then WinPFGW gets caught in an endless loop of Brillart Lehmer tests, anyone who has an idea how to avoid that, because it is getting a pain in the $$s:smile: since I would really like to know for sure which k's is really primed, and bring them to n=25,000. That way we will for sure only have removed k's that is actual primes, hence the value of the evidence is more accurate.

@Rogue: Switching PCtmpString with bignum, still doesn't meet the needings, since it is important that I do not get the decimal expansion of the Prime found but the k*3^n-1 expression of the prime found. This will also save a ton of data.

Thank you for pointing out the need of -f Michaf, had totally sweat that one out of my little head :smile:

Kenneth!

I was thinking that a fixed n sieve would probably be faster, but I don't know the removal rate. For example if you test to n=100, what percentage of k still do not have a prime? What about n=1000? n=10000?

[QUOTE=KEP;134271]@Michaf: I was doing PRP testing of all values untill now. However I still have the problem, when asking following: script.pl -f -tp, it runs 20002 tests and then WinPFGW gets caught in an endless loop of Brillart Lehmer tests, anyone who has an idea how to avoid that, because it is getting a pain in the $$s:smile: since I would really like to know for sure which k's is really primed, and bring them to n=25,000. That way we will for sure only have removed k's that is actual primes, hence the value of the evidence is more accurate.

@Rogue: Switching PCtmpString with bignum, still doesn't meet the needings, since it is important that I do not get the decimal expansion of the Prime found but the k*3^n-1 expression of the prime found. This will also save a ton of data.

Thank you for pointing out the need of -f Michaf, had totally sweat that one out of my little head :smile:

Kenneth![/QUOTE]
Now, a list is created with all PRP's, which can then be confirmed at a later stage. (Only a few, if any will not be primes, so that won't be a problem)

[QUOTE=rogue;134272]I was thinking that a fixed n sieve would probably be faster, but I don't know the removal rate. For example if you test to n=100, what percentage of k still do not have a prime? What about n=1000? n=10000?[/QUOTE]

I've done the following:

testing upto 25k, 2M per day, 2M k's leaving 10 candidates
testing upto 10k, 0.3M per hour 1.5M k's left 30
testing upto 1k, 1M per hour, 10M k's left 2150 remaining
testing upto 100, 86564 per 5 minutes, 367 remaining

so:

25k: 1M takes 12 hours, leaving 5 candidates. The whole range will approx leave: 315k candidates +- 90 CPU years
10k: 1M takes 3 hours, leaving 20 candidates. The whole range will approx leave: 1.3M candidates +- 22 CPU years
1k: 1M takes 1 hour, leaving 2150 candidates. The whole range will approx leave: 140M candidates +- 8 CPU years
100: 1M takes 57 minutes??, leaving 4404 candidates. The whole range will approx leave: 286M candidates +- 8 CPU years

Thoughts:
* Testing to 25k certainly looks ineffecient,
* Testing to 1k looks a tad bit too little to me
* 2150 candidates left are still quite a bunch to process, so I think 10k (5k?) is the way to go
* 1.3M candidates left sounds manageable to me, especially if a sieve can handle say 100k at a time
* testing to 100 is a waste of space :)

@Michaf: Well with the new changes, this is freaking awesome. I will take it to n=1,000 and try to run a batch of 100M. Thanks for your mighty work, really glad that the reductiong has been so great, and that you has coocked up such a program, now I even dare to guess that within 10 years this base 3 will be broken at least for Riesel, but hey it should be weird if reductions want come to the sierpinski :smile:.

Kenneth!

Ps. I'll try to get back to you with some timings :smile: But I think for now, that I'll take the entire range tested to n<=25,000 simply to have as few candidates to test as possible.

It appears that taking 1M towards 25,000 will take about 1 hour, which means 96M k's a day on my Quad :smile: gr8

[QUOTE=KEP;134280]
It appears that taking 1M towards 25,000 will take about 1 hour, which means 96M k's a day on my Quad :smile: gr8[/QUOTE]

What? :) is your quad 12 times faster then my laptop!!??!! :smile:
I'm very amazed...
That would mean, if you'd take it on your own to 10k, you'd 'only' need about 22/12/4=half a year of dedication on your machine!

Can anyone come up with a sensible name for the script?
Using just sierp3, or riesel3 sounds so boring :)

[QUOTE=michaf;134286]What? :) is your quad 12 times faster then my laptop!!??!! :smile:
I'm very amazed...
That would mean, if you'd take it on your own to 10k, you'd 'only' need about 22/12/4=half a year of dedication on your machine![/QUOTE]

It might actually be 12 times faster, but I think you might have checked or tested on a lower range, where the primes were differently n'ed. At a closer look, I could see that from n=100M to n=100.25M almost all primes were below n=100. So maybe when I starts working really hard on my Dual core in about 5-7 days, we can get a more accurate timing, and then I will run an entire range of 10M, and note the starting time, and then when it finishes, I'll be able to finally know exactly how long this will take. Realisticly, I think that we are talking around endings of 2009 then all k's remaining will have been taken to 25,000. I'm considering to test to n=<2,500 since this will leave around 40 k's per million or maybe 400 (I don't remember), but times saved on using srsieve and then switch to WinPFGW once sieving is at optimal depth is just grand, compared to bringing it up to 25,000 n.

Actually just think I'll do a test run of a 1 million range. It should either way be able to finish tomorrow :)

Kenneth!

Ps. Suggestion for name: Very desctructive counter conjecture script :smile: or plain k_killer... I dunno, but someone may come up with a really great name eventually mine is after all also a bit lame!

Second edit: It appears that going to n<=5,000 for each k will leave around 20 candidates per million. This however can be reduced, when dividing the candidate k's with 3 (k mod 3 = 0 then del), either way 100 of thousands is left at n<=5,000 for the entire range, but maybe this can be used for testing the sievelimit for srsieve :smile:

Wow, I got so lost in all of this. If anyone has anything specific to a status, that is k-range and n-range that has been tested and what k's are remaining, I'll list them on the web pages.

As for k's remaining, to list them all, I'd have to ask that they be searched to at least n=5K and even better n=10K first. I don't want to get into listing 1000's or 10000's of k's and then removing multitudes of them as we go higher...too much maintenance is required.

I would be OK with just stating the NUMBER of k's remaining at a given search limit for a specific k-range, even if the search limit is small such as n=1000. When calculating the number of k's remaining, please make sure and remove any k's that are divisible by 3^q (where q>=1) if k / 3^q yields a k-value that is also remaining.


Thanks,
Gary

[QUOTE=gd_barnes;134306]Wow, I got so lost in all of this. If anyone has anything specific to a status, that is k-range and n-range that has been tested and what k's are remaining, I'll list them on the web pages.

As for k's remaining, to list them all, I'd have to ask that they be searched to at least n=5K and even better n=10K first. I don't want to get into listing 1000's or 10000's of k's and then removing multitudes of them as we go higher...too much maintenance is required.

I would be OK with just stating the NUMBER of k's remaining at a given search limit for a specific k-range, even if the search limit is small such as n=1000. When calculating the number of k's remaining, please make sure and remove any k's that are divisible by 3^q (where q>=1) if k / 3^q yields a k-value that is also remaining.


Thanks,
Gary[/QUOTE]

Well I'm going to search all k's to n<=25,000. This should ultimately have us end up with ~315,000 k's remaining (before div 3) if the conjecture is not even more reduced. I'm considering to run a lot of ranges of k's up to n<=5000, propably 50 or so, since that will leave 2000 candidates, that I'll then sieve. Maybe I'll go even further k's and sieve a lot more k's from n<=5,000 to n<=25,000.

About maintenance, there may still be a lot, but at least I think we will be able to progress pretty fast once I get this conjecture to n<=25,000. I just has to run around 6300 ranges (of 10M k's), so really not a big deal anymore to do work on this k.

Hope it all made sence.

Regards

Kenneth!

[quote=KEP;134321]Well I'm going to search all k's to n<=25,000. This should ultimately have us end up with ~315,000 k's remaining (before div 3) if the conjecture is not even more reduced. I'm considering to run a lot of ranges of k's up to n<=5000, propably 50 or so, since that will leave 2000 candidates, that I'll then sieve. Maybe I'll go even further k's and sieve a lot more k's from n<=5,000 to n<=25,000.

About maintenance, there may still be a lot, but at least I think we will be able to progress pretty fast once I get this conjecture to n<=25,000. I just has to run around 6300 ranges (of 10M k's), so really not a big deal anymore to do work on this k.

Hope it all made sence.

Regards

Kenneth![/quote]


OK, fire away. Right now, I'm assuming that your last status stands. That is that you have tested up to k=2M and n=25K with 6 k's remaining and of course that you'll be searching ALL k-values. If you see anything that you'd like me to update on the web pages, let me know.

Micha, I am taking it by your conversation with Kenneth that you are OK letting him do the entire Riesel base 3. With automated scripts in hand on a high-speed machine, it will be interesting to see what he can do since the conjecture is now at a manageable level.

Kenneth, one warning from experience: It can get VERY boring finding hundred of thousands and millions of small primes for months at a time. You may find that you want to do like Micha and I are going to do on the Sierp side. That is search for small primes to k=50M, sieving all the k's remaining, test up to k=50M for higher primes while searching k=50M-100M for small primes, etc. My eyes are about to glaze over from the Sierp k<30M effort that I'm finally about done with. lol

One thing that I find that people underestimate on prime searching in general: The boredom factor surrounding searching for extremely huge primes (takes so long to search one) or searching for huge numbers of very small primes (takes so long to finally get up to the interesting primes). Both make it much more difficult to continue with any one effort so you have to have a good mix of different efforts in order to stay with them all.


Gary

@Gary:

OK I'll fireaway. About boredom, this is actually why, I will run my own project for the next 3-26 weeks, mostly because this keeps me from dying out of boredom and also it gives me time to prepare the thousands of script files needed and the total of 4-6 batch files needed, to spread the conjecture over all 6 cores. I know that everything can get boring, but thinking about the fact that I'm going to find thousands of primes maybe even millions, actually also gives a great chance to test out srsieve and its limits, so actually something new can come out of it :smile:

You can by the way, aswell as other can, follow the progress with the Riesel Base 3 Conjecture on my website, which will be updated once every week or every second week (promise). Maybe you can post a link to my website on your Riesel site, Gary?

Actually I think that Michafs script and the command-line version of WinPFGW, should offer us some great opportunities for having PrimeGrid help us tackle the Sierpinskis, but who knows they are also building up more and more work with only a very little flow of people coming to their aid :smile:

Take care everyone.

Kenneth!

I've found by my program this new record Sierpinski value for base=3:
1694420352676*3^n+1 is composite for all n values. The covering set is
5,7,13,19,37,41,73,757,6481

new record Sierpinski value for base=7:
1112646039348*7^n+1 is composite for all n values. The covering set is
5,13,19,37,43,73,181,193,1201

[QUOTE=R. Gerbicz;134340]I've found by my program this new record Sierpinski value for base=3:
1694420352676*3^n+1 is composite for all n values. The covering set is
5,7,13,19,37,41,73,757,6481

new record Sierpinski value for base=7:
1112646039348*7^n+1 is composite for all n values. The covering set is
5,13,19,37,43,73,181,193,1201[/QUOTE]

Congrats and thanks :)

That's quite a difference from the last conjecture base 3, a 3000 times reduction :smile: 'only' 26 times the effort for riesel 3, but surely manageable!

base 7 is a magnitude harder still, due to the larger base, but also, doable within a few thousand cpu-years (I'll give it a go to test how much will be left for base 7)

[QUOTE=R. Gerbicz;134340]I've found by my program this new record Sierpinski value for base=3:
1694420352676*3^n+1 is composite for all n values. The covering set is
5,7,13,19,37,41,73,757,6481

new record Sierpinski value for base=7:
1112646039348*7^n+1 is composite for all n values. The covering set is
5,13,19,37,43,73,181,193,1201[/QUOTE]

Totally great! Such a breathtaking reduction in base 3.

[QUOTE=michaf;134344]Congrats and thanks :)
base 7 is a magnitude harder still, due to the larger base, but also, doable within a few thousand cpu-years (I'll give it a go to test how much will be left for base 7)[/QUOTE]

Hmm.. I can't seem to get the modular restricions in as easy as I thought...
[QUOTE]div=powmod(k,1,3);
if(div=1) {
k+=2;
goto start;
}
[/QUOTE]

doesn't work :(

Again, new record for Sierpinski, base=3:
1125458784774*3^n+1 is composite for all n values.
Covering set=5,7,13,17,19,37,41,73,193,757

[QUOTE=R. Gerbicz;134360]Again, new record for Sierpinski, base=3:
1125458784774*3^n+1 is composite for all n values.
Covering set=5,7,13,17,19,37,41,73,193,757[/QUOTE]

Wow another reduction by half a trillion k's :smile:, really awesome what you accomplish here, this is really helpfull, wonder if you actually overtakes my effort on riesel base 3, if you magically comes up with another reduction :smile:...

Now I'm just wondering, is there someway to make this a distributed effort, in order to find more covering sets or can the tast of finding covering sets only be at one machine at a time? Also how do you start this search, from lowest k and up or from conjectured k and then goes down?

Regards

Kenneth!

[QUOTE=KEP;134374]
Now I'm just wondering, is there someway to make this a distributed effort, in order to find more covering sets or can the tast of finding covering sets only be at one machine at a time? Also how do you start this search, from lowest k and up or from conjectured k and then goes down?
[/QUOTE]

New record for Sierpinski base=3 !
125050976086*3^n+1 is composite for all n.
covering set=5,7,13,17,19,37,41,193,757

Small correction:
For the above posted Sierpinski base=7 record k=1112646039348
this is a smaller covering set: 5,13,19,43,73,181,193,1201

Now you can also enjoy the search! (I've stopped it.)

I've uploaded my code, you can download it: [URL="http://robert.gerbicz.googlepages.com/covering.c"]http://robert.gerbicz.googlepages.com/covering.c[/URL]
And an exe optimized by flags for P4: [URL="http://robert.gerbicz.googlepages.com/covering.exe"]http://robert.gerbicz.googlepages.com/covering.exe[/URL]

The program requires 5 integers to start:
exponent base C primebound best

where we are testing exponent, it means that the period of the covering set's length will be this number (or it's divisor),
known good examples are those where this number has got lots of small divisors, say exponent=24,72,144,...

base is the base of the sequence

C is 1 for Sierpinski, -1 for Riesel, it means we are testing k*b^n+C sequence (it isn't interesting, but
you can use other values also)

primebound: up to this number we consider all primes which divides b^exponent-1, I've used 10000,
you can use larger/smaller values for it, but very large, say 1000000 is obviously inefficient and slow down the program

best: upper bound for the k value, we are searching k values for that k<best.
It's good to set it to the best knwon k+1.

Note that the product of the last two parameters should be < 2^62, otherwise it'll be an integer overflow.
(For our search it isn't very interesting.)
I think up to base<2^15 the program is good.


Here are some examples to (re)discover currently known record solutions:
24 15 1 10000 100000000000000
find in 1 second k=91218919470156 for exponent=24,
base=15, 1 so Sierpinski, prime bound=10000, best k=100000000000000

24 7 1 10000 2000000000000
find in 1 second k=1112646039348 for exponent=24,
base=7, 1 so Sierpinski, prime bound=10000, best k=2000000000000

144 3 1 10000 126000000000
find (this took about half an hour or so) k=125050976086 for exponent=144,
base=3, 1 so Sierpinski, prime bound=10000, best k=126000000000

24 7 -1 10000 410000000000
find in 1 second k=408034255082 for exponent=24,
base=7, -1 so Riesel, prime bound=10000, best k=410000000000

Robert

I am so happy you have posted a windows executable! I am planning to research base 3 some more.

Do you have any timings for your programme when you get into larger "exponents" such as 330 or 2310, as 3^11-1 brings in two smallish primes, 23 and 3851?

[QUOTE=robert44444uk;134424]Robert

I am so happy you have posted a windows executable! I am planning to research base 3 some more.

Do you have any timings for your programme when you get into larger "exponents" such as 330 or 2310, as 3^11-1 brings in two smallish primes, 23 and 3851?[/QUOTE]

It's hard to predict the timing. I would try only those exponents, which are divisible by 24, all recently found record solutions have period length divisible by 24! So 330,2310 aren't a very good run. Yes, they bring in 23, but lots of small primes are excluded from the covering set, see the listed primes if you run the program.

[quote=R. Gerbicz;134425]It's hard to predict the timing. I would try only those exponents, which are divisible by 24, all recently found record solutions have period length divisible by 24! So 330,2310 aren't a very good run. Yes, they bring in 23, but lots of small primes are excluded from the covering set, see the listed primes if you run the program.[/quote]
is there any sort of counter u can put on

[QUOTE=R. Gerbicz;134425]It's hard to predict the timing. I would try only those exponents, which are divisible by 24, all recently found record solutions have period length divisible by 24! So 330,2310 aren't a very good run. Yes, they bring in 23, but lots of small primes are excluded from the covering set, see the listed primes if you run the program.[/QUOTE]

But I won't feel comfortable unless all k up to n=330 or 2310 (or any other value for that matter) are tested and all remaining k are shown not to have a simple covering set.

I am nervous because CRM does provide unpredictable results, and it is possible that, with the mods all lining up, a quite low value might pop out as a solution, despite the superficially unattractive modulo order of the candidate cover set primes and mod requirements for each prime.

[QUOTE=robert44444uk;134431]But I won't feel comfortable unless all k up to n=330 or 2310 (or any other value for that matter) are tested and all remaining k are shown not to have a simple covering set.

I am nervous because CRM does provide unpredictable results, and it is possible that, with the mods all lining up, a quite low value might pop out as a solution, despite the superficially unattractive modulo order of the candidate cover set primes and mod requirements for each prime.[/QUOTE]

As I read on this topic Simelink tried all exponents up to 144 for Riesel type, for base=3,7,15 by his program. You can do it on the Sierpinski type, that wouldn't take so much time, I haven't done that, in fact I've checked only about 10 different exponents for these hard bases on the Sierpinski side. So there can be low exponents which give better k values.

i'm testing sierp base 3 ... first results:

[QUOTE]covering
144
3
1
100000
1694420352677
Checking k*3^n+1 sequence for exponent=144, bound for primes in the covering set=100000, bound for k is 1694420352677
Examining primes in the covering set: 13,5,7,41,757,73,17,193,19,37,6481,97,577,769
And their orders: 3,4,6,8,9,12,16,16,18,18,24,48,48,48
**************** Solution found ****************
1125458784774
**************** Solution found ****************
405697492212
**************** Solution found ****************
135232497404
**************** Solution found ****************
125050976086

[/QUOTE]

i continue up to exponent = ? and i will edit the above quote ...

[QUOTE=michaf;134344]
base 7 is a magnitude harder still, due to the larger base, but also, doable within a few thousand cpu-years (I'll give it a go to test how much will be left for base 7)[/QUOTE]

For Sierpinski base 7:

I've managed to get a modular in... a % was hidden in the docs :>
Results:

100000 k's tested to n=1000, takes about 5 minutes, leaving 20 k's

This is about the same ratio as for base 3.
The time taken is much larger due to the larger base.

so: 1112646039348 will leave about 222M candidates
and will take about 105 CPU years

[QUOTE=robert44444uk;133966]You might also put your program to work to look at Sierpinski base 3, where a lot of work has been done, but you might be able to do better than the mooted k
3574321403229074.

also other Sierpinskis
base 7, k value 162643669672445
base 15, 91218919470156
base 71, 5917678826

Chris Caldwell would be interested in your results if you beat these.

Also there is a real challenge to see if you can use partial covering sets created by algebra, as x^n+1 often factors algebraically. This is especially relevent to x^3+1 which should provide algebraic factors, but I have been stumped in my efforts to make this work.[/QUOTE]

Robert, where can I find a list of all known conjectures, if there is such thing? Google seems to be oblivious of the fact that one might come in handy :)

[quote=michaf;134468]Robert, where can I find a list of all known conjectures, if there is such thing? Google seems to be oblivious of the fact that one might come in handy :)[/quote]
How 'bout the Conjectures 'R Us web pages? (The link is right under the Conjectures 'R Us subforum name on the forum home page.) :smile:

[QUOTE=Anonymous;134470]How 'bout the Conjectures 'R Us web pages? (The link is right under the Conjectures 'R Us subforum name on the forum home page.) :smile:[/QUOTE]

Yep, but not for bases like 71 :wink:.
(It goes only to base 31, thought it can of course be expanded)...

My gish! This work is unbelievable!! Congrats Mr. Gerbicz on a tremendous contribution to the project and the math community!!


Gary

[quote=michaf;134475]Yep, but not for bases like 71 :wink:.
(It goes only to base 31, thought it can of course be expanded)...[/quote]

Prof. Caldwell has an unpublished math paper that he sent me shortly after the project started on the Sierpinski side only. It lists conjectures for all bases <= 100. I do not know if he wished the paper to be public info. so if you'd like some conjectured values from it, I'll send him a note asking if it's OK to reveal that info.

That said, the conjectures get smaller as the bases get bigger and hence become easier to calculate. I, personally, came up with the conjectures on many of the Riesel and Sierp bases <= 32 (I didn't have the paper before I started the project) because they weren't clear in many of the threads here or elsewhere. But I used no math in doing so. I just used srsieve for 100000 k-values at a time and sieved to n=25K after removing k's with a trivial factor. Whatever the lowest k-value that it dropped from the sieve (shown in srsieve.out) was the conjecture. It was quite simple but didn't work so well when the conjecture was k>3M. It simply took too long.

There is one more thing I'd like to bring up here. I would prefer if we avoided continuing to start on new bases. Could we please hold off on k=7 and 15 for now? It is a very large administrative effort on my/our part here each time a new base is started, especially on bases with large conjectures or that are not very prime bases...recent examples are bases 3 and 19. Also, I haven't even had a chance to review the new base 25 work done by Siemlink, which has many primes from base 5 that can be used to eliminate some k-values. The effort it takes to verify and make sure everything is as correct as possible is very large for such bases. Even on a lesser base, Riesel base 24, it took several hours to come up with the correct algebraic factors for it that effectively eliminated 26 k-values in order to avoid future unnecessary work.

I never thought I'd suggest limiting anyone's work anywhere here but on this immense project, there is SO MUCH work remaining on the bases that we have searched already and we need to put more resources into searching higher n-ranges in many of the bases as well as the many bases that only have from 1-3 k's remaining so that we can prove some of the conjectures.

I'm very much in favor of the programming it takes to lower the conjectures so by all means, continue with that. But I'd just as soon that we hold off on doing any primality searching on any more new bases for now.

And finally...I do not consider base 3 or 19, Riesel or Sierp, to be a 'new' base at this time. Once the effort is out of the way to get them started, the ongoing maintenance is generally much less.


Thank you,
Gary

[QUOTE=michaf;134468]Robert, where can I find a list of all known conjectures, if there is such thing? Google seems to be oblivious of the fact that one might come in handy :)[/QUOTE]

You might want to write to Chris Caldwell, as he has a number of his students working on the Sierpinski side. For Riesels I am not aware of any materials other than what we see here.

[QUOTE=R. Gerbicz;134433]As I read on this topic Simelink tried all exponents up to 144 for Riesel type, for base=3,7,15 by his program. You can do it on the Sierpinski type, that wouldn't take so much time, I haven't done that, in fact I've checked only about 10 different exponents for these hard bases on the Sierpinski side. So there can be low exponents which give better k values.[/QUOTE]

Robert

I am having problems running the covering.exe program

I type in the command such as: D:\ covering 4 8 1 100 100000000 and get no response, just a move of the cursor to the next line. Looking at tneural's output makes me think that you programme is supposed to respond with some screen outputs, but I get nothing. And the CPU does not appear to be used, which means I am doing something fundamentally wrong.

I am using an AMD ML 40.

Maybe it is not supposed to work on this type of machine.

[QUOTE=robert44444uk;134523]Robert

I am having problems running the covering.exe program

I type in the command such as: D:\ covering 4 8 1 100 100000000 and get no response, just a move of the cursor to the next line. Looking at tneural's output makes me think that you programme is supposed to respond with some screen outputs, but I get nothing. And the CPU does not appear to be used, which means I am doing something fundamentally wrong.

I am using an AMD ML 40.

Maybe it is not supposed to work on this type of machine.[/QUOTE]

Yes, it isn't compiled for amd. If somebody could compile it for amd also it would be great.

[quote=robert44444uk;134523]Robert

I am having problems running the covering.exe program

I type in the command such as: D:\ covering 4 8 1 100 100000000 and get no response, just a move of the cursor to the next line. Looking at tneural's output makes me think that you programme is supposed to respond with some screen outputs, but I get nothing. And the CPU does not appear to be used, which means I am doing something fundamentally wrong.

I am using an AMD ML 40.

Maybe it is not supposed to work on this type of machine.[/quote]
it uses the stdin to get the integers from

[QUOTE=R. Gerbicz;134527]Yes, it isn't compiled for amd. If somebody could compile it for amd also it would be great.[/QUOTE]

Thank you for coming back to me Robert so soon, at least it is not some stupid error on my behalf.

[QUOTE=gd_barnes;134519]
There is one more thing I'd like to bring up here. I would prefer if we avoided continuing to start on new bases. Could we please hold off on k=7 and 15 for now? It is a very large administrative effort on my/our part here each time a new base is started, especially on bases with large conjectures or that are not very prime bases...recent examples are bases 3 and 19. Also, I haven't even had a chance to review the new base 25 work done by Siemlink, which has many primes from base 5 that can be used to eliminate some k-values. The effort it takes to verify and make sure everything is as correct as possible is very large for such bases. Even on a lesser base, Riesel base 24, it took several hours to come up with the correct algebraic factors for it that effectively eliminated 26 k-values in order to avoid future unnecessary work.
[/QUOTE]

Gary, I have absolutely NO intentions on starting on either of those bases, it was just plain curiosity if they were also 'very prime'. (And for bases >31, I didn't know such a list existed, and was just curious)

So, sit back and take a deep breath... :wink:

next time I program
 

my program isn't finished yet. I am planning to include a base range as well. But first I want it quicker....

Willem.

[quote=michaf;134571]Gary, I have absolutely NO intentions on starting on either of those bases, it was just plain curiosity if they were also 'very prime'. (And for bases >31, I didn't know such a list existed, and was just curious)

So, sit back and take a deep breath... :wink:[/quote]


AHHHHHHHHHHHHHHHH!!!!!!!

I can feel the fresh ocean breeze as I sit back and take in its relaxing aroma amid the lack of new bases started.

[QUOTE=michaf;134571] And for bases >31, I didn't know such a list existed, and was just curious [/QUOTE]

I looked at a variety of bases originally that might not provide terribly convenient covering sets - but it should be easy to conclude that for all bases above a specific and small integer, that a maximum of 12-cover exist for all values, and in many cases this is 2,3,4 or 6-cover:

Factor b^1-1 and the prime factors provide values that are not useful for covering sets.

Factor b^12-1 and find five new prime factors - because each of b^2-1, b^3-1, b^4-1 and b^6-1 introduces one new prime factor, (with b<>2^i-1 where i is an integer), and these factors provide at maximum 12-cover.

Looking at b=2^i-1, i integer, therefore, is the remaining interesting area for covering sets, as b^2-1 does not provide extra prime factors.

I think the smallest covering sets for the first few values of i are as follows:

i b=2^i-1 smallest cover

3 7 24
4 15 24?
5 31 12
6 63 12
7 127 6
8 255 6
9 511 24
10 1023 3
11 2047 6
12 4095 6
13 8191 12
14 16383 3
15 32767 12
16 65535 12
17 131071 3
18 262143 6
19 524287 6
20 1048575 4
21 2097151 6
22 4194303 3
23 8388607 4
24 16777215 6

I wonder if b=511 is the largest base with cover greater than 12?

For non b=2^i-1, as b gets larger it is really hard to find values where the smallest cover set is 12, as b^3-1, b^4-1, b^6-1 must only produce 1 new prime at each step up. An example is b=47110, with new primes introduced at

n new prime factor
1 3,41,383
2 47111
3 739799737
4 2219352101
6 2219304991

[QUOTE=robert44444uk;134523]Robert

I am having problems running the covering.exe program

I type in the command such as: D:\ covering 4 8 1 100 100000000 and get no response, just a move of the cursor to the next line. Looking at tneural's output makes me think that you programme is supposed to respond with some screen outputs, but I get nothing. And the CPU does not appear to be used, which means I am doing something fundamentally wrong.

I am using an AMD ML 40.

Maybe it is not supposed to work on this type of machine.[/QUOTE]


the command you use is not working

i use this:
[CODE]covering [ENTER]
exponent [ENTER]
base [ENTER]
riesle/sierp [ENTER]
prime range [ENTER]
best vaue found [ENTER]
[/CODE]
after the 6th [ENTER], the program start ...

it's a lot of manual work, but i had time to try up to 431 (432 running at the moment) no better results at the moment !

For me worked:

covering (enter)
4 8 1 100 100000000 (enter)

program works...
program ends...

arrow up (enter) (this gives again covering
arrow up (this gives the same input, you only need to change the exponent)

[quote=michaf;134641]For me worked:

covering (enter)
4 8 1 100 100000000 (enter)

program works...
program ends...

arrow up (enter) (this gives again covering
arrow up (this gives the same input, you only need to change the exponent)[/quote]


Is there a way to turn this into a batch process? I tried this in a file I called batch.bat:
covering
4 8 -1 10000 1000000
covering
6 8 -1 10000 1000000
.
.
.
(etc.)

I then typed 'batch' at the command line and it executed the 'covering' program but it then waits for input from me. That is it won't get the input from the 2nd line.

Is there a way to tell it to accept the input from the 2nd line? I also tried "covering 4 8 -1 10000 1000000" all on each line of the batch file, the same as what Robert used at the command line for a non-batch process, and had the same problem that he did. It just ignores the rest of the line after the 'covering' command.


On another note, here are a couple of enhancements that I might suggest (if not already suggested):

Allow a range of exponents to be entered and write the output to a file. Perhaps by a 6th input such as in:
4
144
8
-1
10000
1000000



So the above would test exponents 4 thru 144 and write the output to some .txt file.

Thanks for a great program!


Gary

[quote=gd_barnes;134659]Is there a way to turn this into a batch process? I tried this in a file I called batch.bat:
covering
4 8 -1 10000 1000000
covering
6 8 -1 10000 1000000
.
.
.
(etc.)

I then typed 'batch' at the command line and it executed the 'covering' program but it then waits for input from me. That is it won't get the input from the 2nd line.

Is there a way to tell it to accept the input from the 2nd line? I also tried "covering 4 8 -1 10000 1000000" all on each line of the batch file, the same as what Robert used at the command line for a non-batch process, and had the same problem that he did. It just ignores the rest of the line after the 'covering' command.[/quote]
Try this:

echo 4 8 -1 10000 1000000 | covering
echo 6 8 -1 10000 1000000 | covering

...and etc. for the rest of the commands in the batch file.

Change the first few lines of the main() function to this:
[code]
int main(int argc, char *argv[])
{

int N,b,C,v[32],w[32],A[32],L,LC,limit,temp,i,j,p,add,len;
int pos,test,res,ord,all,p2,possible,e,*S,*R,**RES,**RES2,stored_LC[32];
long long int best;
long long int alpha,alpha2,beta,M,K,E;
char word[32];

if (argc == 6)
{
N = atol(argv[1]);
b = atol(argv[2]);
C = atol(argv[3]);
limit = atol(argv[4]);
strcpy(word, argv[5]);
}
else
scanf("%d%d%d%d%s",&N,&b,&C,&limit,word);[/code]
then it will take arguments from the command line.

I suspect that using the FPU for the numerous mods in the code could double performance.

[QUOTE=Anonymous;134661]Try this:

echo 4 8 -1 10000 1000000 | covering
echo 6 8 -1 10000 1000000 | covering

...and etc. for the rest of the commands in the batch file.[/QUOTE]

Great, this works on my AMD. Happy puppy now

Astonishing software!!!!!

@ Everyone: Really great work you all do here. I can tell you, that if really wanna work on a huge base please consider run k-ranges above 500M k for base 3 riesel. If you use Michafs program, it will bring you fast in progress. However for the next month or so, no k above 500,000,000 for riesel base 3 will be worked at. So if you take any of the work above that k-range please just drop a note here, and I'll catch it before starting the next ranges.

On a sidenote, it takes ~315 MB of RAM to sieve 50,000 k's from n=1 to n=25,000 using srsieve.exe, but besides from that it causes no problems to run that many candidates and test them using srsieve.exe! Also on another note, due to memory issues, it is not recommended to use sr2sieve.exe since it requires about 700MB of RAM for every 1,500 k's. Whatever you decide any one of you, it really means a lot, of course if anyone brings the conjecture below k 500,000,000... well then please consider use your ressources somewhere else :smile:

Have a nice weekend, all of you, and Gary your very welcome, the least I could do was to send you the sieved files that I had, since no one really has to do more sieve when it was in fact at optimal depth at least for base 12 sierpinski. Good luck on finding a prime or at least take this big and huge leap in the Base 12 sierp testing, just hope you can do it without you or your computer gets hurt :smile:

Regards

KEP

For Robert Gerbicz

Robert: Is there a way you can have a "autosave" file with the program?

I am still wading through base 3, but I get stuck on covering sets where the size of the set has a lot of factors, like 336 (programme running for 2 days so far)

If I get a power cut longer than my battery capacity, then I will lose and have to start over.

No improvements to those already posted noted to date, but I skipped a couple of long running numbers because of power cuts.

What about a reservation thread? I would like to join the fun because I don't know who is running what! Thank you.

[QUOTE=gd_barnes;133988]I agree with this. The new Riesel base 3 value for the project is now 63064644938. Proof:
Gary[/QUOTE]

This values for this and the Riesel were discovered by Klasson in Sept 2004 - see

[url]http://tech.groups.yahoo.com/group/primeform/message/4698[/url]
[url]http://tech.groups.yahoo.com/group/primeform/message/4708[/url]

The post 4713 suggests the Riesel might indeed be the minimum, checked to multiplicative order 200.

[QUOTE=robert44444uk;135225]This values for this and the Riesel were discovered by Klasson in Sept 2004 - see

[url]http://tech.groups.yahoo.com/group/primeform/message/4698[/url]
[url]http://tech.groups.yahoo.com/group/primeform/message/4708[/url]

The post 4713 suggests the Riesel might indeed be the minimum, checked to multiplicative order 200.[/QUOTE]

Ooops , should have read post 11 here first!!!

[QUOTE=robert44444uk;133966]

also other Sierpinskis
base 7, k value 162643669672445
base 15, 91218919470156
base 71, 5917678826

[/QUOTE]

Sierpinski 7 result 1112646039348

Covering 24-set 19,5,43,13,181,1201,73,193 in positions 1,3,2,12,6,1,5,21

Don't know how Chris Caldwell's students missed this one

[quote=robert44444uk;135386]Sierpinski 7 result 1112646039348

Covering 24-set 19,5,43,13,181,1201,73,193 in positions 1,3,2,12,6,1,5,21

Don't know how Chris Caldwell's students missed this one[/quote]
read post 54

[QUOTE=henryzz;135399]read post 54[/QUOTE]

Thanks Henryzz, should pay more attention. Age catching up with me!!

[quote=KEP;135844]Regarding the Riesel Base 3:

I'm not going to take the Riesel Base 3 above k=500,000,000. So for fairness I'm unreserving all k above 500M and keeping my reservation for all k<=500M. It has turned out to involve a great bit more work than I nescessarialy is willing to provide, and also a fact is if I'm going to complete all k's stated by the conjecture for now, the conjecture want be taken to n<=25K for all k's for at least 15-30 years from now.

Now some timings: Expect every 100 million k's to take up about 1 month of computation time.

But to sum up, the Riesel Base 3 is now availeable for everyone for k>500M. Thanks for understanding.

In case you may wonder what else I'm going to do, I will most likely spend the next 3-4 month working on the base 19 sierpinski. And maybe once I complete my reservation for Base 19 sierpinski I might extend it if further k's remain. Else I will propably do something else usefull :smile:

Take care everyone.

Kenneth![/quote]


OK, I'll note this on the reservations page.

I told you finding millions of small primes would get boring after a while! :grin:

Since this involves reservations, I'll move it over to the reservations thread. We're using this thread for discussion about the conjecture values.

Thanks for the update and good luck on Sierp base 19! It may turn out to take more total CPU time than Riesel base 3 because it's not a very prime base.


Gary

[quote=em99010pepe;135082]What about a reservation thread? I would like to join the fun because I don't know who is running what! Thank you.[/quote]


Carlos,

What would you like a reservations thread for?

Are you referring to the search of lower conjectured values using the new software introduced here? If so, I could probably set up something for that.


Gary