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-   -   Sierpinski / Riesel - Base 22 (https://www.mersenneforum.org/showthread.php?t=6916)

 michaf 2007-11-25 10:01

You can take them,

I cannot get to the computer I tested them on right now, but my guess is that I updated the web-page when I stopped searching.
Good luck!

and @Gary:
apologies accepted, I think the comments were made with the best intentions :)

As for including or not: You might want to just a side-note telling the story, it'll be clear to everyone then.

[QUOTE=Siemelink;119113]Michaf, are you still working on this numbers? If not, do you mind if I take over?
In the thread there is a post stating that you tested all until n = 18000.
How far did you get?

Willem.[/QUOTE]

 gd_barnes 2007-11-26 05:21

[quote=michaf;119155]and @Gary:
apologies accepted, I think the comments were made with the best intentions :)

As for including or not: You might want to just a side-note telling the story, it'll be clear to everyone then.[/quote]

OK, thanks for the input, Michaf. In a list of remaining k's to find prime for each base, if there are "exception-situation" k's like this, I will show those with an asterisk by them -or- may not show them but instead put a special note at the bottom of the page about them.

As I get into creating the page, I'll ask people's input about what they think looks the best.

Gary

Found some.

Aloha everyone.

I have some results:
5659*22^97758+1 is probable prime
6462*22^45507+1 is probable prime
1013*22^26067-1 is probable prime
2853*22^27975-1 is probable prime
4001*22^36614-1 is probable prime

Having fun, Willem.
--
Sierpinski / Riesel - Base 22

Conjectured Sierpinski at 6694 [5,23,97]
Conjectured Riesel at Riesel 4461 [5,23,97]

Sierpinski
22 (cedricvonck)
484 (cedricvonck)
1611 (Willem tested upto 98000)
1908 (Willem tested upto 60000)
4233 (Willem tested upto 30000)
5128 (Willem tested upto 30000)

Riesel
3104 (willem tested upto 60000)
3656 (willem tested upto 60000)

 gd_barnes 2007-12-06 03:00

I have some results:
5659*22^97758+1 is probable prime
6462*22^45507+1 is probable prime
1013*22^26067-1 is probable prime
2853*22^27975-1 is probable prime
4001*22^36614-1 is probable prime

Having fun, Willem.
--
Sierpinski / Riesel - Base 22

Conjectured Sierpinski at 6694 [5,23,97]
Conjectured Riesel at Riesel 4461 [5,23,97]

Sierpinski
22 (cedricvonck)
484 (cedricvonck)
1611 (Willem tested upto 98000)
1908 (Willem tested upto 60000)
4233 (Willem tested upto 30000)
5128 (Willem tested upto 30000)

Riesel
3104 (willem tested upto 60000)
3656 (willem tested upto 60000)[/quote]

Great work, Willem! And a top-5000 prime to boot! :smile: Keep us posted on your progress. I'm accumulating all of the info. for bases <=32 into a master spreadsheet that I am using to slowly create some web pages.

Question...were you able to prove the primes? Although it's slow, I use Proth.

Thanks,
Gary

Aah, proving prime with some other program. I didn't think so far ahead yet. Ok, I have proth running now.

Thanks for the tip, laters, Willem.

 rogue 2007-12-06 21:52

You should be able to prove these prime with WinPFGW and it will be much faster than Proth. Use the -tp or -tm switch (depending upon -1 or +1, although I don't recall which switch is used with which sign). Combine it with -f0 and you should be all set.

 axn 2007-12-07 00:37

[QUOTE=rogue;120072]You should be able to prove these prime with WinPFGW and it will be much faster than Proth. Use the -tp or -tm switch (depending upon -1 or +1, although I don't recall which switch is used with which sign). Combine it with -f0 and you should be all set.[/QUOTE]

-tp means "Classic [B]p[/B]lus side test" = N+1 test = applicable for -1 numbers.
Vice versa for -tm

[quote=pfgw documentation]
-t currently performs a deterministic test. By default this is an N-1
test, but N+1 testing may be selected with '-tp'. N-1 or N+1 is
factored, and Pocklington's or Morrison's Theorem is applied. If 33%
size of N prime factors are available, the Brillhart-Lehmer-Selfridge
test is applied for conclusive proof of primality. If less than 33%
is factored, this test provides 'F-strong' probable primality with
respect to the factored part F.
[/quote]

 geoff 2007-12-07 00:52

[QUOTE=gd_barnes;119126]Masser, I checked out the thread that you posted here. It is a good one but I guess I am a little bit confused now. In the post, doesn't Geoff state the following?:

[QUOTE=geoff]
2. k > 0 is a base 5 Sierpinski number if k*5^n+1 is not prime for any integer n >= 0.
...
3. k > 0 is a base 5 Sierpinski number if k*5^n+1 is not prime for any integer n.
...
For the purposes of [b]this[/b] project it makes no difference whether we use definition 2 or definition 3.
[/QUOTE]

I can only speculate and maybe you can confirm that we want to use the above base 5 defintion for all bases. Is that your thinking? If so, here is where I'm confused:
[/QUOTE]

The conclusion above was based on the particular properties of the base 5 sequences (i.e. the primes that had been discovered so far), it does not a priori apply to other bases.

edit: The quote above has been edited, see the [url=http://www.mersenneforum.org/showthread.php?t=4832]original post[/url].

 gd_barnes 2007-12-07 07:52

[quote=geoff;120096]The conclusion above was based on the particular properties of the base 5 sequences (i.e. the primes that had been discovered so far), it does not a priori apply to other bases.

edit: The quote above has been edited, see the [URL="http://www.mersenneforum.org/showthread.php?t=4832"]original post[/URL].[/quote]

Thanks for responding and clarifying Geoff. I'm wondering what properties those were for base 5 and would they apply to at least 'some' other bases such as base 22?

Gary

 gd_barnes 2007-12-07 07:55

[quote=rogue;120072]You should be able to prove these prime with WinPFGW and it will be much faster than Proth. Use the -tp or -tm switch (depending upon -1 or +1, although I don't recall which switch is used with which sign). Combine it with -f0 and you should be all set.[/quote]

Very good. I should have known as much since I've been using PFGW extensively for these conjecture searches but didn't look into all of its options. Thanks for the heads up.

Gary

 kar_bon 2007-12-07 13:24

something like this:

call:
pfgw -tc -q"1468*11^26258+1"

output:
PFGW Version 20031222.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]

Primality testing 1468*11^26258+1 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 100.00% and helper 0.02% (300.02% proof)
1468*11^26258+1 is prime! (813.9536s+0.1133s)

karsten

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