Conjectures 'R Us; searches needed

[geoff]

Originally Posted by gd_barnes

That would be great and it's interesting that you asked. I just run all possible k's that don't have trivial factors through srsieve for the range of n=1-10K up to P=25K; about 100000 k's at a time. Whatever the first k is that it removes from the sieve is the conjecture.

That should work OK, but it is very inefficient because there are a large number of k and only a small range of n, and the algorithm used by srsieve is designed for the opposite situation.

I have found Robert's post and will think about how to automate some of this.

[gd_barnes]

Originally Posted by geoff

That should work OK, but it is very inefficient because there are a large number of k and only a small range of n, and the algorithm used by srsieve is designed for the opposite situation.

I have found Robert's post and will think about how to automate some of this.

Sounds great. That's a nice piece of work by Robert but ultimately I couldn't quite understand all of it well enough to guarantee 100% accuracy in coming up with the conjectures.

About the lack of efficiency of srsieve in that scenario...that was clear but it didn't matter much with what I was running. Over 90% of the time, I just had to run one test and the total run time was generally < 5 mins. for each 100000+ k test. < 10% of conjectures are k>100000. And I wouldn't wait for it to actually save the huge file, which would take many more mins. I'd just hit Ctl-C twice, delete the file, and if no sequence was removed from the sieve, run through the next 100000+ k test.

What we really need a program for at this point are bases 3, 7, and 15 only that I am aware of, although I've only tested all bases up to base 33 plus bases 64, 128, and 256. But it would certainly speed up things when and if we extend to larger bases in the future.


Gary

[Jean Penné]

Hi,

I would be happy to know your opinion about what I posted the 08 Jan 08 :

http://www.mersenneforum.org/showthread.php?t=9830#2

(but perhaps it was misplaced, thus not seen...)

Regards,
Jean

[kar_bon]

i read about your post but no time yet to work with.
it's quite an interesting conjecture to prove and i'm interested in the Riesel odd/even side of this problem. it's worth another extra data page for the RPS site.
will do this for the Riesel power-2 bases for CRUS too next time.
i think i take some searching on 9519, 14361, 19401 and 20049. which ranges you searched yet? any findings?
karsten

[gd_barnes]

Originally Posted by Jean Penné

Hi,

I would be happy to know your opinion about what I posted the 08 Jan 08 :

http://www.mersenneforum.org/showthread.php?t=9830#2

(but perhaps it was misplaced, thus not seen...)

Regards,
Jean

Oh yes, I saw it. I had to think about it before responding and then promptly forgot to respond!

I would be in favor of doing the even conjecture on both sides because it is subset of this project! The even Sierp conjecture is a subset of your Sierp base 4 project. In other words, as stated before, I'll be glad to help coordinate sieving and searching Sierp base 4. But I/we can make k=23451 and 60849 our first priority.

The same applies to Riesel base 4. We (you, in this case because you're searching them) can make k=9519, 14361, 19401 and 20049 a higher priority for Riesel base 4 than the other k's.

Finding a prime for these 6 k's wouldn't prove our conjectures but it would help out a lot and of course it would prove the 'Gallot conjectures'.

I think the odd conjectures would be somewhat outside of the scope of this project so I wouldn't be inclinded to coordinate a search on it (I'm so busy I can't hardly see straight with what we have!). But if you want to create a thread within this project, keep track of everything, and ask people if they'd like to help with sieving/searches, that's fine with me.

I didn't know if you wanted my opinion on doing searches on them or what I thought about the conjectures themselves. I think they were a BRILLIANT piece of work when they came out in 2001. Not so much in today's day and age when they can be easily computed. The even conjectures are just a subset/variation of our current base 4 conjectures and the odd conjectures would be kind of like a base 3.5 or 4.5 conjecture or something similar and could be easily computed by tweaking some of today's software that searches for covering sets.


Gary

[gd_barnes]

I moved some status/reservation posts for Riesel base 4 to that thread.

[gd_barnes]

Originally Posted by Jean Penné

Hi,

I would be happy to know your opinion about what I posted the 08 Jan 08 :

http://www.mersenneforum.org/showthread.php?t=9830#2

(but perhaps it was misplaced, thus not seen...)

Regards,
Jean

Jean,

I just had a small PM exchange with Karsten. Even though it isn't exactly what our project is doing, I think the base 2 odd/even cojectures would be an excellent sub-project for it so that is what we will do.

Karsten has a small web page already set up for it that I think he has now sent you. In a few days or when Karsten feels his web page is ready, I'll add it as a link from some of the current conjectures web pages as well as add its description as a sub-project in our project description.

As I told Karsten, one or both of you are free to create a new thread in this forum to coordinate searches for this if you desire.

Thanks for bringing up this interesting piece of work! The odd conjectures are the most interesting since they are unexplored territory whereas the even conjectures are just subsets of our current base 4 conjectures.

If you really want to take this to the maximum, you could come up with conjectures for k's that only have primes for n==0mod3, 1 mod3, 0mod5, 1mod5, etc., etc. I don't know if that's mathematically reasonable to pursue but it might be interesting to find out.


Gary

[mdettweiler]

Considering that we now have all of this thread's info on the stats pages, should this thread be un-stickied and locked?

[gd_barnes]

Originally Posted by Anonymous

Considering that we now have all of this thread's info on the stats pages, should this thread be un-stickied and locked?

Yeah, that's one of about 25 things on my task list for this weekend! Actually my task was to update the first page here but it's becoming a duplicate maintenance nuisance. There may be some use for the thread in the future so I'll just unsticky it and put a date on the first page that shows when it was applicable.

Good suggestion.


G