Bases 6-32 reservations/statuses/primes

[Siemelink]

Originally Posted by gd_barnes

Please let me know two things: (1) Is there a prime for k=177228? (2) Is your search limit now n=20K?

Thanks,
Gary

Hi Gary,

You are good at this stuff. I completely missed that the base 5 primes with uneven n can still net primes for base 25.

Currently, the effort for base 25 is running on two cores, one from 15,000 up and another from 20,000 down. When that is done I will sieve again to mop up until n = 25,000.

Willem
--
Primality testing 177228*25^15080-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 13, base 1+sqrt(13)
177228*25^15080-1 is prime! (121.5738s+0.0016s)

[Siemelink]

Originally Posted by gd_barnes

In the future, I must have the results files anytime anything is submitted here. It only takes a minute to post them here.

Thanks,
Gary

Hi Gary,

you make a good point. However, my current setup does not allow me to follow this guidance. These machines are behind a firewall that takes away my flexibilty.
What I'll do is that I'll setup an LLR-server. Then I can run my effort as one virtual machine and carry over the data at my leisure.

Willem.

[Siemelink]

Originally Posted by gd_barnes

515756*7^2595-1 is NOT prime! It has a factor of 19.

Gary

Primality testing 515756*7^18902-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 10+sqrt(3)
515756*7^18902-1 is prime! (74.6900s+0.0016s)

No worries, Willem

[gd_barnes]

Originally Posted by masser

IIRC, k=151026 is the only sequence being tested by SRB5 that is divisible by 3.

I had concluded the same thing. It is the only k that I show remaining for base 25 that is being processed by your project and is divisible by 3.

What's interesting about this since it's divisible by 3, you could end up finding a prime that is NOT a base 25 prime because the n-value can be odd or even. It must be even for us. I'll have to keep watch on any primes that you guys find and if k=151026 drops with an odd n-value, then we'll need to pick it up from your n-value / 2.

Thanks for the heads up.


Gary

[gd_barnes]

Willem,

Thanks for the primes on those 2 problem k's for base 7 and 25.

I have now done an official balancing of all k's remaining on Riesel base 25. The only final error I found was my own. I had listed a k-value remaining that there was a prime for. I also removed k=177228 that you just now posted a prime for. This leaves 193 k's remaining for us to search and 90 for the base 5 project to search for a total of 283.

Since it's difficult for you to provide results files, I'm sending some links to some Excel spreadsheets that are what I need whenever you start a new base. I'm going to encourage everyone to start using spreadsheets similar to this for new bases.

What I've failed to impart on people on new bases is that they can be tremendously tedious and are really like doing accounting. (no offense to any accountants out there) The thing is, you have to account for a disposition of EVERY k-value at all points. It does not suffice to send lists of primes > 2K with k's remaining. That leaves many k's unaccounted for.

The key is that ALL k's are accounted for that don't have trivial factors. In our case, it is k==(0 mod 6) and (2 mod 6). For every k that meets those criteria, there must be an accounting done. A k-value can have one of the following dispositions:
1. There is a prime found by us.
2. There is a prime found by another project.
3. It is a multiple of the base with k/b^q still remaining and hence eliminated.
4. It contains algebraic factors and hence eliminated.
5. It is remaining with no known prime.

That is what I did for all 110K+ k-values on Riesel base 25 using my searches up to n=~2.6K, your primes found, the base 5 primes found, and the base 5 k's remaining.

Here is what I need you to do now:

Take a look at the web pages at the 193 k's that are remaining that need to be tested by us. This was concluded after a full accounting and balancing of everything so it should now be error-free. I need you to closely check the k's that you are testing by doing the following:

1. Remove any k's that are remaining and being tested by the base 5 project or have already had primes found by that project.

2. Add any k's that you have failed to test and begin testing them where I left off at n=2.6K. I think there may be serveral that you may have assumed were being done by base 5.

Further, if you can provide me an updated spreadsheet of the status of each of those 193 k's each time you post a group of primes, that would be the best thing. Don't use any spreadsheets I'm sending you at this point. I just need to know the status of each k remaining and I need it sorted by k-value. The status would include that you are continuing to search it or that you have found a prime for it. If a prime, list the n-value of the prime like you've done before. Really the only thing different at this point I need then what you've been providing is that the entire list be sorted by k and not 2 separate lists of k's remaining and primes found.

Here are links to spreadsheets that I used for balancing this:
http://gbarnes017.googlepages.com/pr...se25-0mod3.zip
http://gbarnes017.googlepages.com/pr...se25-2mod3.zip
http://gbarnes017.googlepages.com/Ri...remainGary.zip

If I sound a little dictatorial here, I don't mean to. It's for my own sanity so I don't spend quite so much time verifying new bases.


Thanks,
Gary

[gd_barnes]

Willem,

Another issue: I'm doing primality tests on all primes found for Riesel base 25. I found the following:

117030*25^10678-1 is composite: [11DDCD5E3EA7691E] (30.4127s+0.0013s)
102512*25^15383-1 is composite: [20E28B4FFFAFB0E4] (59.1929s+0.0031s)


For now, I'll leave the k's as not remaining on the web pages. I assume you have the correct prime n-values that you can check real quick.


Gary

[Siemelink]

Originally Posted by gd_barnes

Willem,

Another issue: I'm doing primality tests on all primes found for Riesel base 25. I found the following:

117030*25^10678-1 is composite: [11DDCD5E3EA7691E] (30.4127s+0.0013s)
102512*25^15383-1 is composite: [20E28B4FFFAFB0E4] (59.1929s+0.0031s)

For now, I'll leave the k's as not remaining on the web pages. I assume you have the correct prime n-values that you can check real quick.

Gary

Primality testing 117030*25^10668-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
117030*25^10668-1 is prime! (69.6837s+0.0012s)

I can't find the other one in my primefile, nor in my excel where i copy things. Nor 15383, 153*, anything. So I'll do l = 102512 once again

Willem.

[gd_barnes]

Originally Posted by Siemelink

Primality testing 117030*25^10668-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
117030*25^10668-1 is prime! (69.6837s+0.0012s)

I can't find the other one in my primefile, nor in my excel where i copy things. Nor 15383, 153*, anything. So I'll do l = 102512 once again

Willem.

D'oh! Don't redo k=102512! 102512 == (2 mod 3) so it must have a base 5 prime. Looking on the web page that I previously gave you a link to for the base 5 project, I see:

102512*5^30776-1 is prime

therefore:

102512*25^15388-1 is prime

(A slight division by 2 error or typo on the exponent.)

Primality test:
Primality testing 102512*25^15388-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
102512*25^15388-1 is prime! (300.1143s+0.0028s)

I will change the primes found for k=102512 and 117030 in my files. No additional searching is needed at this point on your end.


Gary

[Siemelink]

Originally Posted by gd_barnes

D'oh! Don't redo k=102512! 102512 == (2 mod 3) so it must have a base 5 prime. Looking on the web page that I previously gave you a link to for the base 5 project, I see:

102512*5^30776-1 is prime
therefore:
102512*25^15388-1 is prime

Gary

Ah, I made a copying error. But as I am not glued to the screen at dinnertime I found the prime myself too:

Primality testing 102512*25^15388-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
102512*25^15388-1 is prime! (133.2294s+0.0016s)

Laters, Willem.

[gd_barnes]

Sierp base 12 at n=167K; no primes; effort temporarily suspended to assist on port 300 at NPLB.

[KEP]

Here is 1 for sierpinski base 19:

646704*19^11205+1

In a few minutes my Quad will start working on the approximately 3.8 million k/n pairs remaining

KEP!