Bases 6-32 reservations/statuses/primes

[VBCurtis]

7367*28^23099-1 is prime.

[tnerual]

2203*28^13911+1 is a probable prime. Time: 102.559 sec.

by the way, all k*28^n+1 are tested up to n=13911

i will reserve the 6 last k for sierpinski base 28 (i will test them 'til i'm bored ) (i'm still testing my other reservations on base 16)

[gd_barnes]

Good finds Curtis and tnerual. Tnerual, I'll just reserve all of the remaining Sierp base 28 k's up to n=25K for you. If you stop before that or go higher, let me know.

Tnerual, can you go ahead and prove the 'probable primes'? They need to be proven and not just a 'probable prime'. The program PFGW can prove them but LLR can not. LLR can only prove bases that are powers of 2 such as your base 16.

The software for PFGW is available for download in the software thread. There are also instructions in the thread there and that come with the program. The interface is easy to use. If you've never used it, here is the command line that you would give it to prove one of your Sierp base 28 primes:

pfgw -q1797*28^5681+1 -f0 -t


The -t command is to prove "+1" primes. A -tp command would be used to prove "-1" primes. The -f0 command tells it to not do any small trial factoring (since it obviously has no small factors).

You can also use the Proth program to prove them. It takes much longer to run but you may find it a little easier to understand. Because it takes longer, Proth is not included in the software thread.

Any questions...feel free to send me a PM or post them right here.


Thanks,
Gary

[tnerual]

done :

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 1797*28^5681+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
1797*28^5681+1 is prime! (17.3788s+0.0025s)

Done.
PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 2203*28^13911+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
2203*28^13911+1 is prime! (97.8790s+0.0016s)

Done.

[tnerual]

i'm sorry to flood the topic

but i have a new prime ...

59890*16^29827+1 is prime! Time : 187.0 sec.

all k*16^n+1 tested up to n=30000 (except the 2 that belongs to other people)

i release all sierpinski base 16 k except k=34543 (tested up to 41220) and k=35320 (tested up to 74269)

(in short, my reservations are now 2 sierpinski base 16 and 6 sierpinski base 28)

[mdettweiler]

Sierpinski Base 16 k=2908 tested up to n=100k, no primes. I'm releasing this k. lresults is attached to this post. (Please note that the lresults is for the entire 25K-100K range, and it includes k=4885 up until a little bit after where I'd previously found a prime on there. Thus, part of my lresults file has already been posted here, but I figured I'd post the whole thing rather than just what hadn't been previously posted.)

I've started work on the Riesel Base 13 k=288 that I'd reserved. I'm surprised that it's taking as long as it is, though; is that just because it's not a power of 2? I know that LLR tests are quicker than PRP tests, but I didn't think they were that much quicker; however, I'm finding that tests that took about 600 seconds for Sierp. Base 16 for the same n-level are taking upwards of 1000 seconds for Riesel Base 13!

[VBCurtis]

Riesel 28:
7367 yielded a prime, noted in primes thread. 6207 complete to 25k, no prime.

Starting 5886 tonight, with the rest of the 5000's to follow. All to 25k. Finding two primes so easily has me fueled to aim for all of Riesel 28 to 25k, but I'll reserve it in chunks in case I get distracted by another new search.

-Curtis

[gd_barnes]

Originally Posted by tnerual

i'm sorry to flood the topic

but i have a new prime ...

59890*16^29827+1 is prime! Time : 187.0 sec.

all k*16^n+1 tested up to n=30000 (except the 2 that belongs to other people)

i release all sierpinski base 16 k except k=34543 (tested up to 41220) and k=35320 (tested up to 74269)

(in short, my reservations are now 2 sierpinski base 16 and 6 sierpinski base 28)

Thank you for flooding the topic. We like a lot of flooding! If you want any more n-ranges of the 'big sieved file', let me know.

I just now posted files for all k's for Riesel base 16 from 'big sieved file 2'. ...also all sieved to P=400G.


Gary

[gd_barnes]

Originally Posted by Anonymous

Sierpinski Base 16 k=2908 tested up to n=100k, no primes. I'm releasing this k. lresults is attached to this post. (Please note that the lresults is for the entire 25K-100K range, and it includes k=4885 up until a little bit after where I'd previously found a prime on there. Thus, part of my lresults file has already been posted here, but I figured I'd post the whole thing rather than just what hadn't been previously posted.)

I've started work on the Riesel Base 13 k=288 that I'd reserved. I'm surprised that it's taking as long as it is, though; is that just because it's not a power of 2? I know that LLR tests are quicker than PRP tests, but I didn't think they were that much quicker; however, I'm finding that tests that took about 600 seconds for Sierp. Base 16 for the same n-level are taking upwards of 1000 seconds for Riesel Base 13!

My experience has been more extreme than yours. Here are some comparisons at different n-levels of LLR prime tests for Sierp base 16 vs. LLR prob prime tests for Riesel base 13:

n-level / Sierp base 16 / Riesel base 13 / ratio
10K 2.9 secs. 8.8 secs. 3.03
25K 19.3 secs. 71.0 secs. 3.68
30K 37.3 secs 104.4 secs. 2.80

For Sierp base 16, this was for k=4885 up to n=25K and k=64815 at n=30K, which is likely why the ratio is less at n=30K. For Riesel base 13, it was all for your k=288.

As you know, this is somewhat an apples-to-oranges comparison but at least it gives a ballpark ratio. To get a true valid comparison, we'd have to adjust the base 13 exponent up by a multiplier of log(16) / log(13) = 1.081.


Gary

[mdettweiler]

Originally Posted by gd_barnes

My experience has been more extreme than yours. Here are some comparisons at different n-levels of LLR prime tests for Sierp base 16 vs. LLR prob prime tests for Riesel base 13:

n-level / Sierp base 16 / Riesel base 13 / ratio
10K 2.9 secs. 8.8 secs. 3.03
25K 19.3 secs. 71.0 secs. 3.68
30K 37.3 secs 104.4 secs. 2.80

For Sierp base 16, this was for k=4885 up to n=25K and k=64815 at n=30K, which is likely why the ratio is less at n=30K. For Riesel base 13, it was all for your k=288.

As you know, this is somewhat an apples-to-oranges comparison but at least it gives a ballpark ratio. To get a true valid comparison, we'd have to adjust the base 13 exponent up by a multiplier of log(16) / log(13) = 1.081.


Gary

Okay, thanks. One more quick question though: Considering how long the tests are taking, do you think I should sieve more? The Riesel Base 13 sieve file is at p=400G; do you think that's enough considering the PRP times I'm getting?

[gd_barnes]

Originally Posted by Anonymous

Okay, thanks. One more quick question though: Considering how long the tests are taking, do you think I should sieve more? The Riesel Base 13 sieve file is at p=400G; do you think that's enough considering the PRP times I'm getting?

Hum...good question. Were you previously implying that you were getting 1000 sec. test time around n=62-63K? I wasn't clear there because my test time for my last test at n=62413 was 447 secs so it sounded a little high.

It may depend on how fast your machine sieves vs. LLR's. If you have a strong sieving machine, then the answer may be yes. Otherwise maybe not.

The case against sieving further is that you're only LLRing a narrower range of n than that which I originally sieved. When I sieved, (if I remember right) I sieved until the removal rate was about 500-600 secs. on my dual-core Dell laptop because I was sieving the range of n=25K=100K and that was just a little less testing time than I got for the 70% range of around n=77K.

I've started sieving to slightly less than what would normally be the optimal sieve depth for the conjecture efforts due to the fact that if a prime is found, the rest of the file is simply wasted. In this case, I still think the optimum sieve may have been only P=500G, but even that would save little additional testing time. Once you get close to the optimum, it doesn't matter a whole lot whether the time is spent sieving or LLRing.


Gary