Why Base 5 and Weights
 

Just curious, why base 5 and not 3 or 7?

Also, could you provide the weights for the remaining k's?

Use : -b5
for
[url]http://pages.prodigy.net/chris_nash/psieve.html[/url]



Citrix
:cool: :cool: :cool:

[QUOTE=Citrix]Use : -b5
for
[url]http://pages.prodigy.net/chris_nash/psieve.html[/url]
[/QUOTE]
I tried this program but I don't know how to interpret the output. This is an example for k=10918:

[code]
$ ./psieve3.exe 10918 -b5

*****************************************
* PSIEVE 3.21 Chris Nash, Paul Jobling *
* Thanks to Joe McLean for suggestions! *
*****************************************

10918
n=1 mod 2 - factor 3
Best % - 50.00 for modulus 2
n=1 mod 3 - factor 31
n=4 mod 5 - factor 11
n=2 mod 6 - factor 7
Best % - 83.33 for modulus 6
n=3 mod 9 - factor 19
n=12 mod 16 - factor 17
n=14 mod 17 - factor 409
Best % - 88.89 for modulus 18
n=6 mod 19 - factor 191
n=0 mod 30 - factor 61
Best % - 90.00 for modulus 30
n=36 mod 42 - factor 127
n=18 mod 42 - factor 43
n=45 mod 69 - factor 139
n=62 mod 82 - factor 83
n=0 mod 89 - factor 179
Best % - 93.33 for modulus 90
n=60 mod 94 - factor 2069
n=20 mod 152 - factor 457
n=91 mod 155 - factor 311
n=120 mod 173 - factor 3461
n=10 mod 188 - factor 12409
n=168 mod 196 - factor 197
n=5 mod 209 - factor 419
n=185 mod 215 - factor 431
n=172 mod 226 - factor 227
n=176 mod 232 - factor 33409
n=138 mod 232 - factor 233
n=33 mod 239 - factor 479
n=17 mod 245 - factor 491
n=176 mod 254 - factor 509
255:254
[/code]
Is 255:254 the weight? I have just been using NewPGen to sieve until now.

You also need to use the -e option. it will in the end say that this many candidates are left, which will be the weight.

Citrix
:cool: :cool: :cool:

Why base 5?
 

In answer to Citrix's point, I had been looking at Sierpinski/Riesels of the form k.(2^x+1))^n+/-1, where x=1,2,3.... because these are the only base forms which give non trivial solutions for k. See [url]http://groups.yahoo.com/group/primeform/message/4773[/url]
and David Broadhurst's elegant reply.

x=0 is the classic series, subject to extensive literature and the the SoB search
x=1 is already being extensively researched and looks horribly difficult because the lowest mooted k is in the 10 million range both Sierpinski and Riesel
the next x=2 is the focus of this search and gives a sensible number of candidates up to the lowest proven values of k both Sierpinski and Riesel, and the Sierpinski is easier because there are less candidates

Hope this answers your point.

Regards

Robert Smith

could you also provide the average and total weight for the remaining k's.

[QUOTE=robert44444uk]In answer to Citrix's point, I had been looking at Sierpinski/Riesels of the form k.(2^x+1))^n+/-1, where x=1,2,3.... because these are the only base forms which give non trivial solutions for k. See [url]http://groups.yahoo.com/group/primeform/message/4773[/url]
and David Broadhurst's elegant reply.

x=0 is the classic series, subject to extensive literature and the the SoB search
x=1 is already being extensively researched and looks horribly difficult because the lowest mooted k is in the 10 million range both Sierpinski and Riesel
the next x=2 is the focus of this search and gives a sensible number of candidates up to the lowest proven values of k both Sierpinski and Riesel, and the Sierpinski is easier because there are less candidates

Hope this answers your point.

Regards

Robert Smith[/QUOTE]

could you provide me a link to where the base 3 search is being done?

Citrix
:cool: :cool: :cool:

[QUOTE=Citrix]could you also provide the average and total weight for the remaining k's.[/QUOTE]
Can you tell me how to calculate them? Under the weight column I have just put the number reported by 'psieve.exe <k> -b5 -e'. [url]http://www.geocities.com/g_w_reynolds/Sierpinski5/status.txt[/url]

just do w1+w2+w3+...Wn to get total
then for average w1+w2+w3+....Wn/n

for n k's left.

I hope this post is more clear.


Citrix
:cool: :cool: :cool:

OK, I see what you mean now. :redface:

[QUOTE=Citrix]could you provide me a link to where the base 3 search is being done?

Citrix
:cool: :cool: :cool:[/QUOTE]

Citrix

See [url]http://groups.yahoo.com/group/primeform/message/4388[/url] and resulting long string of replies

Regards

Robert Smith

[QUOTE=robert44444uk]Citrix

See [url]http://groups.yahoo.com/group/primeform/message/4388[/url] and resulting long string of replies

Regards

Robert Smith[/QUOTE]


Robert,

It would be intresting to see if k's that are multiple of 3 or 5 or both can ever generate a sierpinski or riesel number for base 2? I will try to work on this later this week or as soon as I get some time and see what I can come up with. Base 5 takes too long as most of the optimizations for base 2 that make them super fast don't work for base 5. (I'm not sure if base 4 counts, but the smallest sierpinski number is k=5 for that base and I can prove that :rolleyes: :showoff: :bounce: )

Citrix
:cool: :cool: :cool:

[QUOTE=Citrix]Robert,

It would be intresting to see if k's that are multiple of 3 or 5 or both can ever generate a sierpinski or riesel number for base 2? I will try to work on this later this week or as soon as I get some time and see what I can come up with. Base 5 takes too long as most of the optimizations for base 2 that make them super fast don't work for base 5. (I'm not sure if base 4 counts, but the smallest sierpinski number is k=5 for that base and I can prove that :rolleyes: :showoff: :bounce: )

Citrix
:cool: :cool: :cool:[/QUOTE]

I figured out how to generate sierpinski's that are multiples of 3 and 5 for base 2 but it is unlikely that any exist under 2^32, so it would not be feasible to work on that right now either. Base 5 seems the best search right now.


Citrix
:cool: :cool: :cool:

Robert, you can look at base 4 though.

66741 is the smallest sierpinski number for base 4 such that the k is always a multiple of 3 or k=3*h+1. where h is a natural number.

I have tested all the odd numbers, haven't had a chance to test the even k's yet. But there may be a smaller sierpinksi number for base 4.

So there will be fewer numbers k left and at the same time this is basically base 2 so will be 8 times faster than base 5.

I will do more testing on this tonight and post my results.

Citrix
:cool: :cool: :cool:

[QUOTE=Citrix]Robert, you can look at base 4 though.

66741 is the smallest sierpinski number for base 4 such that the k is always a multiple of 3 or k=3*h+1. where h is a natural number.

I have tested all the odd numbers, haven't had a chance to test the even k's yet. But there may be a smaller sierpinksi number for base 4.

So there will be fewer numbers k left and at the same time this is basically base 2 so will be 8 times faster than base 5.

I will do more testing on this tonight and post my results.

[/QUOTE]

Only 37 k left so far. I will work more on this. K are going really fast. The lightest k has a weight of 181 so I should be able to solve this really soon.


Citrix
:cool: :cool: :cool:

How about a project in which base 3 is used, but instead of worrying about actually proving the S/R numbers in each case, the aim of the project would merely be to see how high of a "primeless" k value we can calculate?

So start with k=2,4,6,8... until the project gets "stuck" on a particular k value. Then, the n value would grow and grow until a prime is found for that k value, in which case the project would continue upwards to the next "difficult" k value.

In the process, the project would likely discover some large prime numbers, plus it could assert a minimum bound for the S/P numbers base 3, even if it never does prove either base 3 S/R conjecture.

Here, I'll start the project:

2*3^1+1=7 (prime!)
4*3^1+1=13 (prime!)
6*3^1+1=19 (prime!)
8*3^1+1=25=5*5

So I'm "stuck" on k=8. The exponent will have to be increased until a prime is found, in which case testing on k=10 may begin.

2*3^1-1=5 (prime!)
4*3^1-1=11 (prime!)
6*3^1-1=17 (prime!)
8*3^1-1=23 (prime!)
10*3^1-1=29 (prime!)
12*3^1-1=35=5*7

So I'm "stuck" on k=12. The exponent will have to be increased until a prime is found, in which case testing on k=14 may begin.

[QUOTE=siegert81;364986]
2*3^1+1=7 (prime!)
4*3^1+1=13 (prime!)
6*3^1+1=19 (prime!)
8*3^1+1=25=5*5

So I'm "stuck" on k=8. The exponent will have to be increased until a prime is found, in which case testing on k=10 may begin.

2*3^1-1=5 (prime!)
4*3^1-1=11 (prime!)
6*3^1-1=17 (prime!)
8*3^1-1=23 (prime!)
10*3^1-1=29 (prime!)
12*3^1-1=35=5*7

So I'm "stuck" on k=12. The exponent will have to be increased until a prime is found, in which case testing on k=14 may begin.[/QUOTE]

At the moment, the Riesel side is "stuck" at k=3677878, n=1000000. The Sierpinski side is "stuck" at k=2949008, n=150000. Please have a look at [URL]http://mersenneforum.org/showthread.php?t=9738[/URL] for information. Any help is welcome!

Cool. Well, I'm glad it's being worked on. I'm also glad to see that the S/R numbers for base 3 are only in the billions, as opposed to a 20 digit number!

I may have to return when I buy a new computer...

Base Project
 

[QUOTE=Citrix;47462]Just curious, why base 5 and not 3 or 7?

Also, could you provide the weights for the remaining k's?

Use : -b5
for
[url]http://pages.prodigy.net/chris_nash/psieve.html[/url]



Citrix
:cool: :cool: :cool:[/QUOTE]

Yeah, I agree. We should start a base 3 project and base 7.

Did you look at the link from post 16 (2 posts above yours)?

There's an entire subforum for these projects. Riesel base 3 is nearly tested to 25k, thanks mostly to KEP. See Conjectures R Us.

If you'd just like to find some primes, fire up BOINC and have a go at riesel base 3, or perhaps run a range of 1G from exponent 25,000 to 100,000. Once ranges are tested to 3^100000, I personally sieve from 3^100k to 3^500k and BOINC does the primality testing.

We're not far enough along yet for available testing in the top-5000 range, but that should be ready by fall.

Edit: The crus website linked from the forum lobby is down at present; the host/admin for the project has internet troubles this week. It might be a couple days till you can see the detailed status page for riesel base 3 (R3) or R7 or S3 or S7. R3 has the most work done of the bunch.