Sierp base 3 reservations/statuses/primes

[gd_barnes]

On Sierp base 3, I've now reached k=9M and n=25K.

I've now added a new Sierp base 3 reservations page. 28 k's are remaining as shown on the page.

I will likely start a big sieve after we reach 100 k's remaining.

[gd_barnes]

On Sierp base 3, I'm now up to k=10M and n=25K. 36 k's remaining as shown on the Sierp base 3 reservations page.

I'm taking a break for ~2-3 weeks from this base and then will resume testing by k-value to n=25K until there are 100 k's remaining. That will probably happen between k=15M and 20M.


Gary

[KEP]

Hi Gary. Reserving k 110M-120M for base3 sierpinski conjecture. Thanks for your help. When this range is done, I may consider start a riesel conjecture sieveing. Thanks again. Looking forward to submit my few thousands k's :)

EDIT: Whoops forgot to mention that I take it to 25,000 n!

[gd_barnes]

Originally Posted by KEP

Hi Gary. Reserving k 110M-1110M for base3 sierpinski conjecture. Thanks for your help. When this range is done, I may consider start a riesel conjecture sieveing. Thanks again. Looking forward to submit my few thousands k's :)

EDIT: Whoops forgot to mention that I take it to 25,000 n!

Welcome to the effort KEP! And thanks for asking the detailed questions ahead of time in the PM's.

I'm assuming that you mean k=110M-111M (instead of 110M-1110M). 110M-111M is what your sample script showed in the PM that you sent me.

If so, for a k=1M range, there should be less than 20-30 k's remaining. Base 3 is a VERY prime base! After you're done, you may find that you want to reserve a larger range.

For example, for the range of k=9M-10M for me, there were only 8 k's remaining after a search to n=25K. Of course with higher k's, there will be less chance of each k-value having a small prime so you should have more than that but not many more.


Gary

[KEP]

Hi Gary

I would appreciate if you wrote me down for k=110M to 120M, since I'm working on these 5 ranges. If you would then please tell me if only equal k's has to be tested for the base3 rieselconjecture, then I would like to start a huge attack on this base. Also can I still use the same code in the input file (just changing plus to minus)? But please put me down for the specific k range. Maybe I just rambeled in my reservation. Either way I would like to attack the riesel base3 conjecture when I sometime next week completes this 10M k range :) Thanks for all your understanding and support.

Regards

KEP

[gd_barnes]

Originally Posted by KEP

Hi Gary

I would appreciate if you wrote me down for k=110M to 120M, since I'm working on these 5 ranges. If you would then please tell me if only equal k's has to be tested for the base3 rieselconjecture, then I would like to start a huge attack on this base. Also can I still use the same code in the input file (just changing plus to minus)? But please put me down for the specific k range. Maybe I just rambeled in my reservation. Either way I would like to attack the riesel base3 conjecture when I sometime next week completes this 10M k range :) Thanks for all your understanding and support.

Regards

KEP

OK, I will change your reservation from k=110M-111M to 110M-120M.

I responded to your PM on the Riesel conjecture. The script on the input file would be the same except -1 instead of +1. Like the Sierp conjecture, only even k's need to be tested so no change there.

But there is a slight change on the command line. Instead use:

input.txt -f100 -l100k.txt -tp


The -tp switch tells it to prove the primality of "-1" numbers vs. "+1" numbers.

Good luck and thank you for attacking these huge bases!


Gary

[mdettweiler]

Originally Posted by gd_barnes

<snip>
But there is a slight change on the command line. Instead use:

input.txt -f100 -l100k.txt -tp


The -tp switch tells it to prove the primality of "-1" numbers vs. "+1" numbers.y

Actually, no. -tp signifies that PFGW should do an N+1 test (as opposed to an N-1 test with just plain -t), which can be used for numbers that an N-1 test can't prove primality for. (I've run into those occasionally.) Both N-1 and N+1 tests are not dependent on any form of number, so either should work for both +1 and -1 numbers.

[axn]

Originally Posted by Anonymous

Actually, no. -tp signifies that PFGW should do an N+1 test (as opposed to an N-1 test with just plain -t), which can be used for numbers that an N-1 test can't prove primality for. (I've run into those occasionally.) Both N-1 and N+1 tests are not dependent on any form of number, so either should work for both +1 and -1 numbers.

Actually, to successfully run an N+1 primality test, N+1 must be factored to atleast 33% of its length (meaning, if N is 100 digits, then at least 33 digits worth of prime factorization should be known). Vice versa for N-1. If the 33% factorization criteria is not met, then the test can't "prove" the primality.

Since N+1 factorization of a "-1" number is trivial, it makes sense to use N+1 for "-1" (and N-1 for "+1" numbers).

[mdettweiler]

Originally Posted by axn1

Actually, to successfully run an N+1 primality test, N+1 must be factored to atleast 33% of its length (meaning, if N is 100 digits, then at least 33 digits worth of prime factorization should be known). Vice versa for N-1. If the 33% factorization criteria is not met, then the test can't "prove" the primality.

Since N+1 factorization of a "-1" number is trivial, it makes sense to use N+1 for "-1" (and N-1 for "+1" numbers).

Oh, I see. Thanks for clearing that up!

[paulunderwood]

Originally Posted by gd_barnes

But there is a slight change on the command line. Instead use:

input.txt -f100 -l100k.txt -tp

Are you sure? It is much quicker to do a "probable prime" test than do N+1 or N-1 tests when crunching a batch of numbers. Run the fully blown proving tests on those that the quick tests indicates might be prime. PFGW has a log file for probable primes: "pfgw.log"

Also: why are you not using a sieve instead of "-f"?

[KEP]

Originally Posted by paulunderwood

Are you sure? It is much quicker to do a "probable prime" test than do N+1 or N-1 tests when crunching a batch of numbers. Run the fully blown proving tests on those that the quick tests indicates might be prime. PFGW has a log file for probable primes: "pfgw.log"

Also: why are you not using a sieve instead of "-f"?

Thanks Paul, your post actually just solved the issue mentioned in my previous post. Plus it creates a much smaller log file when doing only PRP tests. So now my command line Gary sounds like this:

"input.txt -l5M.txt" and when done sieving I will use this command line:

"pfgw.log -tp" this will be sufficient and very time consuming, since a lot of tests can very fast be verified up to max n or 25,000 which is my limit :)

So thanks Paul, and of course also to you Gary for helping out that much you did. Maybe if we implemented these lines at all tests, we would really start to see some improvement in speed. Anyway I'll now continue the Base3 attack and launch the major attack from Wednesday, maybe earlier, if I see the Sierpinski range complete in early time :)

Thanks and take care everyone.

KEP!

Ps. Gary you doesn't have to reply to my PMs regarding my problem which is now solved, but if you do that prior to reading this post its also OK, since one enjoys reading science stuff and other peoples solutions to issues occorring :)