Riesel base 3 reservations/statuses/primes

[gd_barnes]

Originally Posted by KEP

@Gary:

About your important 'or', I'm currently running the range 100-110M k, with Michafs script, to n<=5,000. Once they are verified, as the only k's remaining, I was considering to remove all k's that is divisable with the base, which in my case means that they can be k mod 3=0, but if this is not acceptabel (and if it involves to much manual work, though I think a spread sheat should be able to do the work for me pretty fast) I of course not will do it, so if I can get your oppinion on this it would really be appreciated.

Regards

Kenneth

Ps. It may be 14 days to 3 weeks before you really hears back anything from the further work done on the riesel base 3, due to working situations and the fact that I've stucked my Quad with other work for now. Also I have to finish wrapping the base 19 sierpinski to optimal sieve depth, before finally having 1 core availeable (hopefully in one weeks time). But in 3 weeks I may throw in the entire 6 cores. If that doesn't happen, I'll get back to you and we can then decide on how to proceed in the future run (simply to make sure we get somewhere and brings down this conjecture)

No...you can't just remove ALL k's that are divisible by 3. You'll miss some k-values that are remaining. They must be divisible by a POWER OF 3 AND reducable to a k-value that is already remaining. That's because the k divided by a power of 3 may have a prime at ONLY n=1. For example:

Let's say that k*3^1-1 is prime and that is the only known prime for that particular k-value.

Now, let's say that you're searching a k-value that is 3 times the above k-value but you fail to find a prime up to n=10K or n=25K or whatever you're searching to.

It would be incorrect to automatically remove 3k*3^n-1 simply because the k is divisible by 3. We know by the above that 3k*3^0-1 is prime but n must be >= 1 and we have not found a prime for 3k that fits that condition.

One more thing...be sure and reduce the k-value all the way. Sometimes you may not find that k / 3 is remaining but that k / 3^2 or k / 3^3 or k / 3^4 IS remaining. In any of those cases, your k could be removed.

Regardless, removing multiples of the base must be done very carefully. If you are now hesitent to do this, simply attach a spreadsheet of k-values remaining that are divisible by a power of 3 and I'll verify that they can removed. Well over 90% can usually be removed but if you look on the Sierp base 3 reservations page, you'll find that probably 10-15 of them ARE divisible by 3 for just the above reason, simply because k/3 had a prime at only n=1.

About what Micha said, it's OK if you leave a k-value in where we already know a large prime exists, whether it be on top-5000 or found by someone in this project. We'll find it eventually. But removing one where there isn't a known prime simply because it is divisible by 3 would be bad.


Gary

[KEP]

@Gary: I think given the fact that it really doesn't give that much difference in sieving speed, that I'll just (at least for n<=25,000) keep all the k's remaining and take them all to n<=25,000 simply to avoid mistakes

Thanks for your feedback.

Kenneth!

[gd_barnes]

Originally Posted by KEP

@Gary: I think given the fact that it really doesn't give that much difference in sieving speed, that I'll just (at least for n<=25,000) keep all the k's remaining and take them all to n<=25,000 simply to avoid mistakes

Thanks for your feedback.

Kenneth!

Without a doubt, that is the best way to search them. It's too much effort to pull them out ahead of time. What I was referring to was AFTER the search and when you actually report them as remaining here. That is when I remove multiples of the base if they can or k-values with previously known large primes.


Gary

[KEP]

Originally Posted by gd_barnes

Without a doubt, that is the best way to search them. It's too much effort to pull them out ahead of time. What I was referring to was AFTER the search and when you actually report them as remaining here. That is when I remove multiples of the base if they can or k-values with previously known large primes.


Gary

OK, as long as we are clear ... however I think, because I'm not sure if I've removed 1 k that shouldn't have been removed for k<=1M, that I'll eventually do a doublecheck, but not for the moment. If anyone takes the double check, please e-mail me: kenneth 010982 @ g mail . com!

Thanks.

Kenneth!

[Siemelink]

201886*3^39101-1
301096*3^49050-1
731636*3^37215-1
993424*3^25296-1
1512358*3^63729-1
1728886*3^32283-1

are all primes, by way of srsieve -> sr1sieve -> LLR -> PFGW

Enjoy, Willem

[KEP]

Originally Posted by Siemelink

201886*3^39101-1
301096*3^49050-1
731636*3^37215-1
993424*3^25296-1
1512358*3^63729-1
1728886*3^32283-1

are all primes, by way of srsieve -> sr1sieve -> LLR -> PFGW

Enjoy, Willem

Great work Willem, this actually means, that Gary can now at least for the next 3-4 weeks keep a neet ZERO k's remaining below 2M k. Now can anyone doublecheck if k 1816974 can actually be removed from the remaining list (I guess with the primes you had found), since this one particular k was removed when I still thought that k mod 3 = 0 could be removed without a problem, which it later on has shown it can't

But again great work, hope you can kill the 1,500 primes I'll submit (approximately) or maybe 3,000 k's before removed doubles coming in 4 weeks (maybe 3). In case you run out of work, please feel free to attack the ranges of k's for base 3 riesel with k greater than 1500 M and bring them to 25,000 at first.

Actually I think from a sieving point of view, that we would be far better of, if we actually tested the remaining 62.5G k's up to n<=25,000 and then made a combined sieving effort to n<=50,000 since its always faster to sieve more candidates (according to what I've been told way back) than to sieve just part of a range at a time. Also with the few candidates seeming to remaining (less than 250,000) it shouldn't be claiming much on the RAM use. Sieving 50,000 base 3 k's for 25,000 n required on my machine ~163 MB of RAM as of testing of today.

So any chance you join me in this combat?

[KEP]

I've now decided to run the Riesel Base 3 up to at least 1.5 G, so in 8 hours please consider this range as in progress aswell. So therefor if you decide to join in the effort, please consider for Riesel Base 3 to do work on k's above k 1,500,000,000.

Thank you.

KEP!

[gd_barnes]

Originally Posted by Siemelink

201886*3^39101-1
301096*3^49050-1
731636*3^37215-1
993424*3^25296-1
1512358*3^63729-1
1728886*3^32283-1

are all primes, by way of srsieve -> sr1sieve -> LLR -> PFGW

Enjoy, Willem

Nice work Willem! You and Rogue are our k slayers!

If you want, take a hack at the Sierp side of things on a few of the smaller 240 k's remaining at n=25K.

Originally Posted by KEP

Great work Willem, this actually means, that Gary can now at least for the next 3-4 weeks keep a neet ZERO k's remaining below 2M k. Now can anyone doublecheck if k 1816974 can actually be removed from the remaining list (I guess with the primes you had found), since this one particular k was removed when I still thought that k mod 3 = 0 could be removed without a problem, which it later on has shown it can't

But again great work, hope you can kill the 1,500 primes I'll submit (approximately) or maybe 3,000 k's before removed doubles coming in 4 weeks (maybe 3). In case you run out of work, please feel free to attack the ranges of k's for base 3 riesel with k greater than 1500 M and bring them to 25,000 at first.

Actually I think from a sieving point of view, that we would be far better of, if we actually tested the remaining 62.5G k's up to n<=25,000 and then made a combined sieving effort to n<=50,000 since its always faster to sieve more candidates (according to what I've been told way back) than to sieve just part of a range at a time. Also with the few candidates seeming to remaining (less than 250,000) it shouldn't be claiming much on the RAM use. Sieving 50,000 base 3 k's for 25,000 n required on my machine ~163 MB of RAM as of testing of today.

So any chance you join me in this combat?

I agree from an efficiency standpoint, it makes sense to sieve them all at once but like Willem, I found it fun to find a few higher primes, which is why there are no k-values remaining for k<2.9M for Sierp base 3.

One more thing, k=1816974 is not considered remaining because k=201886 WAS remaining and 201886*3^2=1816974. And now that k=201886 has a prime at n=39101, then k=1816974 has a prime at n=39099.

So, I'm confused as to why you say that k=1816974 needs to be checked? It would have been removed from your processing list after you found that k=201886 was still remaining.

It's either one or the other but not both, otherwise we end up doing large amounts of duplicate work for n>25K. That is if k=201886 has a prime for n<=2 but k=1816974 has no primes for n>=1, then k=1816974 is remaining. If k=201886 has no prime, then k=201886 is remaining and not k=1816974.

Because, as you found, it's easier to search all even k's for n<=25K, we do so even though there is some duplicate work on multiples of the base. It's after we are done with that initial process that we are eliminating multiples of the base in the 90-95% of the situations that we can do so. And we do it then because doing duplicate work with long testing times would be extremely inefficient. It's better to take the time to manually remove them as testing times get longer.


Gary

[KEP]

@Everyone: Due to a loss of interest, and the fact that I would seriously like to get going with one of my older projects, I've decided to bring the Riesel Base 3 k no further than k<=1500M. So to anyone willing to take over the k's above, feel free to start doing so. I will still complete the entire range up to k 1,500,000,000 all the way up to n<=25,000. However this is all expected to be done and completed in at most 4 weeks.

Good luck on processing the remaining k's and remove those k's left. Maybe I check back at later basis, but for now consider that running to be the only one. And of course I will continue on my dual in 4 weeks or so to try and bring down the sierpinski base 19.

Regards!

KEP!

[KEP]

Originally Posted by KEP

@Everyone: Due to a loss of interest, and the fact that I would seriously like to get going with one of my older projects, I've decided to bring the Riesel Base 3 k no further than k<=1500M. So to anyone willing to take over the k's above, feel free to start doing so. I will still complete the entire range up to k 1,500,000,000 all the way up to n<=25,000. However this is all expected to be done and completed in at most 4 weeks.

Good luck on processing the remaining k's and remove those k's left. Maybe I check back at later basis, but for now consider that running to be the only one. And of course I will continue on my dual in 4 weeks or so to try and bring down the sierpinski base 19.

Regards!

KEP!

Please excuse me, but I seriously lost interest, so for now at least, I'll only take this Base 3 Riesel to k<=500M and n<=25000. Sorry for leaving, but I just need a break where I consult my old projects and gives them a boost, and also it is better if I start doing some serious work on the sierpinski base 19, before my reservation stalls and I might forget about it.

But still good luck folks on bringing down these hard and "easy" conjectures. And who knows maybe see you again in the future. Also Gary, the 18..... k for riesel base 3 with k<=2M was eluded by myself at n<=5000 testing, so even though it remained in the list before I removed it and stoped LLR testing on this candidate because it essentially were the same, no prime will have been missed... sorry if this caused confusion.

Regards

KEP!

[KEP]

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

Take care everyone.

Kenneth!