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-   -   Sierpinski base 4 (https://www.mersenneforum.org/showthread.php?t=3630)

 Jean Penné 2007-11-28 14:10

My status to-day...

k=18534 is up to n=1,800,342 no prime, continuing...

k=23451 is up to n=1,916,312 no prime, continuing...

k=60849 is up to n=1,864,566 no prime, continuing...

Question : how far is now the last one, k=64494?

When n=2,000,000 reached, I will stop, and it will be necessary to split the work, and better organize the tasks...

Regards,
Jean

 jasong 2007-11-29 05:33

[QUOTE=Jean Penné;119426]When n=2,000,000 reached, I will stop, and it will be necessary to split the work, and better organize the tasks...

Regards,
Jean[/QUOTE]
Just to let you guys know, I'm interested in combined sieving when this happens.

[QUOTE=Jean Penné;119426]
Question : how far is now the last one, k=64494?
[/QUOTE]

k=64494 is up to n=1,766,066 no prime continuing.....

still slowly proceeding further....

-Tyler

 gd_barnes 2007-12-17 04:48

I am keeping the status of your guy's effort in the new "Conjectures 'R Us" effort on the following web pages along with conjectures for all other bases <=32.

I thought you might want to see the info. that I have in the pages regarding this project. If you see any problems with it, let me know. The n-limits searched on all bases are in the base that is being searched. So your limits shown are n=900.2K, 958.2K, 932.3K, and 883K base 4.

This effort also impacts base 16 Sierp for only k=23451 so that would be a great one to find a prime for.

I know this is an official top-5000 project and we have it shown as such. I'll check this thread from time-to-time to get status updates to keep the pages up to date.

Thanks,
Gary

[QUOTE=tcadigan;121164]actually I think I'll take you up on that. I need a break from the base 4 stuff for a bit anyway. I'll do 7773 until n=100K base 16 attached is the latest dat file for my base 4[/QUOTE]

I'm taking a bit of a break with base 4.

reported stopping with Gary in other thread as well as posting the latest npg.

good luck Jean!

 Jean Penné 2008-01-07 14:18

To day status

k = 18534 is up to n = 1939086 no prime...

k = 23451 is up to n = 1945288 no prime...

k = 60849 is up to n = 1900206 no prime...

As I said several times, I will continue these k's up to the top of this range, so n = 2000000,

and then stop, whatever a prime is found or not!

For the continuation of this project, I would prefer we keep the official one active, but will follow the choice of the majority...

In all cases, I think the prime proving work must not be continued alone, and the presieved file must now be splitted, as for the 321 project or others...

The opinions of all other participants are now welcome!

Regards,

Jean

 gd_barnes 2008-01-07 17:15

[quote=Jean Penné;122378]k = 18534 is up to n = 1939086 no prime...

k = 23451 is up to n = 1945288 no prime...

k = 60849 is up to n = 1900206 no prime...

As I said several times, I will continue these k's up to the top of this range, so n = 2000000,

and then stop, whatever a prime is found or not!

For the continuation of this project, I would prefer we keep the official one active, but will follow the choice of the majority...

In all cases, I think the prime proving work must not be continued alone, and the presieved file must now be splitted, as for the 321 project or others...

The opinions of all other participants are now welcome!

Regards,

Jean[/quote]

Jean,

Thank you for the update. I will see if anyone would be interested in pitching in on a coordinated sieve in the 'Conjectures 'R Us' (CRUS) project. I would also agree that your big project should be kept open but I have no problem helping coordinate it since it coincides with our project. Our project will certainly face the same problem in the future on many bases.

I have a couple of unrelated questions...First, were you testing k=19464 for Riesel base 4? It is a multiple of the base (MOB) that I have not included with CRUS yet. If so, I will show it reserved for you on the Riesel base 16 reservation page, where it is not a MOB. That way we won't duplicate your effort for it in our upcoming team drive #2.

I am in the process of putting together a list of k's that are MOB for all bases that we have so far excluded from CRUS but that have no known prime. There are surprisingly few of them. There are only about 4-5 of them on the Riesel side (out of about 25 bases that I've checked) and none affect whether a conjecture has been proven. On the Sierp side, all that I have found have been GFN's so far.

For Riesel base 4, I confirmed your analysis that k=19464 is the only MOB that needs a prime. For Sierp base 4, the only MOB without a prime nor trivial factors is GFn k=65536 but it can't possibly have a prime with current knowledge/technology. It converts to 2^(2n+16)+1, which is effectively proven composite to n=2^32-9. So technically Sierp base 4 cannot be proven.

Here is the 2nd question...While it makes sense to include MOBs in the conjectures, it seems reasonable to exclude GFNs as a requirement for the proof. Do you know if any thought has been given to the idea of excluding GFNs from the conjecture proofs? If so, it would allow the near-future proof of many bases that would otherwise be impossible to prove at this time. Bases that I am aware of with this problem are 4, 6, 10, 16, 18, 22, 32, and 128, which includes all b<=32 and all b=2^m up to b=256. There may be more than these but these are all that I can remember at the moment.

Thanks,
Gary

 Jean Penné 2008-01-07 20:08

[QUOTE=gd_barnes;122395]Jean,

Thank you for the update. I will see if anyone would be interested in pitching in on a coordinated sieve in the 'Conjectures 'R Us' (CRUS) project. I would also agree that your big project should be kept open but I have no problem helping coordinate it since it coincides with our project. Our project will certainly face the same problem in the future on many bases.

I have a couple of unrelated questions...First, were you testing k=19464 for Riesel base 4? It is a multiple of the base (MOB) that I have not included with CRUS yet. If so, I will show it reserved for you on the Riesel base 16 reservation page, where it is not a MOB. That way we won't duplicate your effort for it in our upcoming team drive #2.

I am in the process of putting together a list of k's that are MOB for all bases that we have so far excluded from CRUS but that have no known prime. There are surprisingly few of them. There are only about 4-5 of them on the Riesel side (out of about 25 bases that I've checked) and none affect whether a conjecture has been proven. On the Sierp side, all that I have found have been GFN's so far.

For Riesel base 4, I confirmed your analysis that k=19464 is the only MOB that needs a prime. For Sierp base 4, the only MOB without a prime nor trivial factors is GFn k=65536 but it can't possibly have a prime with current knowledge/technology. It converts to 2^(2n+16)+1, which is effectively proven composite to n=2^32-9. So technically Sierp base 4 cannot be proven.

Here is the 2nd question...While it makes sense to include MOBs in the conjectures, it seems reasonable to exclude GFNs as a requirement for the proof. Do you know if any thought has been given to the idea of excluding GFNs from the conjecture proofs? If so, it would allow the near-future proof of many bases that would otherwise be impossible to prove at this time. Bases that I am aware of with this problem are 4, 6, 10, 16, 18, 22, 32, and 128, which includes all b<=32 and all b=2^m up to b=256. There may be more than these but these are all that I can remember at the moment.

Thanks,
Gary[/QUOTE]

Thanks, Gary, for helping us, it will become more and more necessary!

About your first question, yes, I tested k = 19464 for Riesel base 4, for now, up to n = 137112 (base 2) no prime (I can only progress slowly for Riesel tests, as long as my current Sierpinski ranges are not completed)...

About the second question, when the base is a power of two, there may be MOB k values which are also power of two, and then the candidates are not only Generalized Fermat Numbers, but very Fermat Numbers, so, I think these k's should be excluded (It is conjectured that there are a finite number of Fermat primes, and most of the mathematicians believe that F4 = 65537 is the largest one...).
As I remarked in another thread, proving that F4 is the largest Fermat prime is equivalent to proving that 65536 is an even Sierpinski number...
But, if so, the covering set would be infinite, because it is well known that Fermat numbers are pairwise coprime...

Regards,
Jean

 gd_barnes 2008-01-08 06:24

Conjecture proofs definition verification needed..

[quote=Jean Penné;122412]Thanks, Gary, for helping us, it will become more and more necessary!

About your first question, yes, I tested k = 19464 for Riesel base 4, for now, up to n = 137112 (base 2) no prime (I can only progress slowly for Riesel tests, as long as my current Sierpinski ranges are not completed)...

About the second question, when the base is a power of two, there may be MOB k values which are also power of two, and then the candidates are not only Generalized Fermat Numbers, but very Fermat Numbers, so, I think these k's should be excluded (It is conjectured that there are a finite number of Fermat primes, and most of the mathematicians believe that F4 = 65537 is the largest one...).
As I remarked in another thread, proving that F4 is the largest Fermat prime is equivalent to proving that 65536 is an even Sierpinski number...
But, if so, the covering set would be infinite, because it is well known that Fermat numbers are pairwise coprime...

Regards,
Jean[/quote]

I can't guarantee help in the very near future but I'm sure we can find someone who will at least do some sieving in the future. I'm thinking that getting it set up on an LLRNet server may be the best option after getting the sieving done. I know little about it but I know several people who have plenty of knowledge. What would you think about that?

One more quick question: Do you intend to test k=19464 until you find a prime or is there a limit that you will be searching it to?

I'm glad to hear that you think GFn's should be excluded from the conjectures. I'll ask a couple of other people who may have some input in a new thread here in 'other projects'.

Thanks,
Gary

 Jean Penné 2008-01-08 07:51

[QUOTE=gd_barnes;122449]I can't guarantee help in the very near future but I'm sure we can find someone who will at least do some sieving in the future. I'm thinking that getting it set up on an LLRNet server may be the best option after getting the sieving done. I know little about it but I know several people who have plenty of knowledge. What would you think about that?

One more quick question: Do you intend to test k=19464 until you find a prime or is there a limit that you will be searching it to?

I'm glad to hear that you think GFn's should be excluded from the conjectures. I'll ask a couple of other people who may have some input in a new thread here in 'other projects'.

Thanks,
Gary[/QUOTE]

I intend to test k=19464, and also the other k's I reserved for Riesel base 4, up to n = 524288 base 2 (262144 base 4) if no prime, and, indeed, stopping each k at first prime found! I think it would not be reasonable to continue further alone...

Regards,
Jean

 jasong 2008-01-13 03:51

Would it be possible to set up one computer as an LLRNet server for all these bases, and put each base, plus or minus 1, on different ports? I'm thinking, though I'm not a programmer, that the way the numbers are transmitted could be changed slightly to account for the different combinations. Also, it would be cool if people could get involved in more than one of these sub-projects on one core.

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