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

[michaf]

Originally Posted by michaf

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)

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

[michaf]

Originally Posted by robert44444uk

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.

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 :)

[mdettweiler]

Originally Posted by michaf

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 :)

How 'bout the Conjectures 'R Us web pages? (The link is right under the Conjectures 'R Us subforum name on the forum home page.)

[michaf]

Originally Posted by Anonymous

How 'bout the Conjectures 'R Us web pages? (The link is right under the Conjectures 'R Us subforum name on the forum home page.)

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

[gd_barnes]

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


Gary

[gd_barnes]

Originally Posted by michaf

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

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 Caldwell has an unpublished math paper that he sent me shortly after the project started on the Sierpinski side only.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

[robert44444uk]

Originally Posted by michaf

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 :)

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.

[robert44444uk]

Originally Posted by R. Gerbicz

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.

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.

[R. Gerbicz]

Originally Posted by robert44444uk

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.

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

[henryzz]

Originally Posted by robert44444uk

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.

it uses the stdin to get the integers from

[robert44444uk]

Originally Posted by R. Gerbicz

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

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