Sierp base 3 reservations/statuses/primes

[gd_barnes]

Admin edit: Separated Riesel base 3 reservations/statuses/primes posts from Sierp base 3 reservations/status/primes posts.

Sierp base 3 tested by k-value up to k=2.2M.

With help from the top-5000 site, ZERO k's REMAIN!! surprised

Reserving Sierp base 3 by k-value from k=2.2M-100M. I'll test them all to n=25K if necessary.


Gary

[michaf]

Originally Posted by gd_barnes

Sierp base 3 tested by k-value up to k=2.2M.

With help from the top-5000 site, ZERO k's REMAIN!! surprised

Reserving Sierp base 3 by k-value from k=2.2M-100M. I'll test them all to n=25K if necessary.


Gary

Zero?? :) I expected a few hundred, maybe even less after your previous post... but zilch?

The less the merrier...

[michaf]

I'll be trying out testing Sierp base 3 from k=100M to k=110M (upto n=25k)
(I've tested 100M to 100.01M, and it left zero candidates)

[gd_barnes]

Originally Posted by michaf

I'll be trying out testing Sierp base 3 from k=100M to k=110M (upto n=25k)
(I've tested 100M to 100.01M, and it left zero candidates)

Yep, base 3 is a very prime base. There's just so MANY k's! You could easily do k=100M-100.1M in < 1 day and have no remaining k's.

What helped me out is the top-5000 site, which knocked out 4 k's whose first prime was apparently n>87K. The largest prime that I had to personally find was k=966536 at n=49292. I didn't even have to sieve. I just set PFGW to test them all up to n=50K (not the most efficient way, but the most hassle-free). I would then watch it from time-to-time and when it hit one that was on the top-5000 site, I'd let it double-check it to n=25K to see if it found a smaller prime. If not, I'd stop it and start with the next even k.

But I've FINALLY hit a snag on one and I'm sieving it now to n=200K. k=2290976 is composite to n=57K. I suppose I should just let it go for now and continue on with so many k's but I'm trying to keep my perfect record intact. (lol)

I'll probably try to 'solve' the first 2-3 of them that go beyond n=50K and that aren't on top-5000 by sieving and LLRing but after that, I'll just let them go because it's much more efficient to sieve multiple k's together.

I may start a informal 'team drive' for this but without the usual sieved files. We'll just reserve ranges of k-values and test them up to some predetermined limit using PFGW. n=25K is probably a good choice.


Gary

[michaf]

The way I was thinking about it:

Process a chunk of 1M, 10M or 100M k's to n=25k with pfgw. (On my laptop, it slows down incredably with more then 1M... I'll need to try on my desktop)
and report the remaining k's which have no primes upto 25k here.

Keep a record of those, and sieve them as we get say 100 of them, and test to 100k

The remaining we keep again until we'll have 100 again, and sieve them to n=1M (or 500k, or whichever is the most efficient...)

This way, we'll slowly crawl along on the conjecture, and get top5000 primes in the end with enough sieving done.

(The numbers are of course variable, and depending on how much is left after the initial sieving, I reckoned 100 is plenty for the time being...)

[gd_barnes]

That sounds good to me. Yes, 100 k's at a time for sieving sounds like a good number. Much more just takes too darned long.

I'm being stubborn on my one k=2290976 that I haven't been able to find a prime for yet. I sieved it for n=50K-200K and am LLRing it...currently at n=82K with no prime, but I know that's not the most efficient way to do things in the long run.

I'll be on vacation in Mexico from 3/13-3/19. I'll stop k=2290976 in the morning before I leave. I'm hoping to get it up to n=100K. While I'm gone, I'll just set my machine to only search to n=25K and then I'll determine the missing k's when I get back for inclusion in a future 'big sieve'.


Gary

[gd_barnes]

Sierp base 3 continues its "perfect" streak with:

2290976*3^94265+1 is prime

This was a very lucky find. I had sieved this k to n=200K but only planned to LLR it to n=100K so the prime came just in time.

All k's have now been checked to k=2.4M with ZERO k's STILL remaining! Other large first primes for k>2M are:

2257826*3^42721+1 -and-
2363776*3^20423+1

I've actually tested all k on this base to k=8M and n=25K. There are going to be several k's remaining for k>2.4M but not a huge number of them. I need to do some fancy sorting of output primes files to determine what is left. I'll post the remaining k's later tonight here and on the web pages. When we get to 100 of them, we'll start a mass sieve for n=25K-200K or something similar.


Gary

[gd_barnes]

I sorted the output primes files for Sierp base 3 up to k=3M tested to n=25K. There are FINALLY 3 k's remaining:

2930054
2949008
2980832


There were 6 k's remaining in my file at n=25K for k=2.4M-3M. One was once again knocked out by the top 5000 site: 2621746*3^119335+1 is prime. Two others were multiples of the base but effectively duplicated earlier high primes.

I need to come up with a better way to sort these huge primes files because it is taking much too long to parse and sort them in Excel 50000 k's at a time.

If anyone has a suggestion, let me know. My testing is past k=8M and it's going to take a long time to sort these things to see what k's don't have primes. k=3M-8M is ~2.5M k's and I can't easily get around Excel's 65536-line restriction.


Gary

[IronBits]

Excel 2007: 1,048,576 rows by 16,384 columns, 17,179,869,184 cells.(what a boost!)

That or learn Access

Send me a couple small sample files so I can see what you are doing to sort them.
Maybe a piece of perl code or something could do it more efficiently...
If you are using an Excel formula, then Perl, or something similar, should be able to do the same thing.

[Siemelink]

Originally Posted by gd_barnes

I need to come up with a better way to sort these huge primes files because it is taking much too long to parse and sort them in Excel 50000 k's at a time.

If anyone has a suggestion, let me know. My testing is past k=8M and it's going to take a long time to sort these things to see what k's don't have primes. k=3M-8M is ~2.5M k's and I can't easily get around Excel's 65536-line restriction.
Gary

When I was playing with base 3 I used these two scripts:
ABC2 $b*3^$a-1 // {number_primes,$b,1}
a: from 1 to 2500
b: from 2 to infintity step 6

ABC2 $b*3^$a-1 // {number_primes,$b,1}
a: from 1 to 2500
b: from 6 to infintity step 6

This minimizes the duplicate tests:
- only even k
- no (k mod 3) = 1
- no multiples of 3

I like this because I can run the script for as long as I want. For such a gigantic range "Fire and Forget" is very important and maintenance should be as low as possible. When the pfgw.out file gets too large, filter out all the candidates with:
grep 2500-1 pfgw.out
This spits out only those k where the n reached 2500.

Hope it helps, Willem.

[gd_barnes]

Originally Posted by Siemelink

When I was playing with base 3 I used these two scripts:
ABC2 $b*3^$a-1 // {number_primes,$b,1}
a: from 1 to 2500
b: from 2 to infintity step 6

ABC2 $b*3^$a-1 // {number_primes,$b,1}
a: from 1 to 2500
b: from 6 to infintity step 6

This minimizes the duplicate tests:
- only even k
- no (k mod 3) = 1
- no multiples of 3

I like this because I can run the script for as long as I want. For such a gigantic range "Fire and Forget" is very important and maintenance should be as low as possible. When the pfgw.out file gets too large, filter out all the candidates with:
grep 2500-1 pfgw.out
This spits out only those k where the n reached 2500.

Hope it helps, Willem.

Very interesting but is this for Riesel base 3? If so, you would not test much of what is needed. The logic is what is needed for Sierp base 7, i.e. the elimination of odd k's and k's where k==(2 mod 3). Contrary to you saying it eliminates k==(1 mod 3), it actually eliminates k==(2 mod 3).

For Riesel base 3, there are two problems:

1. We do need to test k==(2 mod 3). Only odd k have a trivial factor for base 3 on both sides. so 2*3^n-1, 8*3^n-1, 14*3^n-1, etc. or the equivalent for the Sierp side should be tested.

2. We can't automatically and easily eliminate all k's divisible by 3 because where k*3^n-1 only yields a prime at n=1, 3k*3^n-1 still has no prime so must be tested. Or if k*3^n-1 only yields a prime at n=2, 9k*3^n-1 still has no prime so must be tested, etc. It's the multiples of the base (MOB) problem. Can you get around that issue?

I know of no command to tell it to ONLY process a 3k if k has a prime for n=1 -or- to NOT process a 3k if k has a prime for n>1 or k does NOT have a prime! It's a tricky issue to say the least!


The script that I use for Sierp base 3 is a simple one that tests everything we need. It does incorrectly duplicate the 3k tests in most cases but correctly processes the 3k's that would be missed by your script:

ABC2 $b*3^$a+1 // {number_primes,$b,1}
a: from 1 to 25000
b: from 2 to 3574321403229073 step 2


Thanks for the advice on the grep command on the pfgw.out file. I wasn't aware of it. I haven't been creating a pfgw.out results file because it's gets HUGE too quickly and time-consuming to pull up and review for k's remaining. But this definitely makes the case for creating the file and using it. I'll try that.

In a synopsis, I think we have to stick with the script I'm using but I should create a results file and use the grep command on it.

Thanks a bunch. That helps a lot.


Gary