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Old 2005-01-02, 07:54   #1
Citrix
 
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Default 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
http://pages.prodigy.net/chris_nash/psieve.html



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Last fiddled with by Citrix on 2005-01-02 at 08:05
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Old 2005-01-03, 02:54   #2
geoff
 
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Quote:
Originally Posted by Citrix
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
Is 255:254 the weight? I have just been using NewPGen to sieve until now.
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Old 2005-01-03, 14:23   #3
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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.

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Old 2005-01-06, 19:53   #4
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Default 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 http://groups.yahoo.com/group/primeform/message/4773
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
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Old 2005-01-18, 22:40   #5
Citrix
 
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could you also provide the average and total weight for the remaining k's.
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Old 2005-01-18, 23:14   #6
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Quote:
Originally Posted by 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 http://groups.yahoo.com/group/primeform/message/4773
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 provide me a link to where the base 3 search is being done?

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Old 2005-01-19, 14:51   #7
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Quote:
Originally Posted by Citrix
could you also provide the average and total weight for the remaining k's.
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'. http://www.geocities.com/g_w_reynold...ki5/status.txt
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Old 2005-01-19, 15:46   #8
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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.


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Old 2005-01-19, 16:04   #9
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OK, I see what you mean now.
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Old 2005-01-19, 16:24   #10
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Quote:
Originally Posted by Citrix
could you provide me a link to where the base 3 search is being done?

Citrix
Citrix

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

Regards

Robert Smith
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Old 2005-01-20, 17:50   #11
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Quote:
Originally Posted by robert44444uk
Citrix

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

Regards

Robert Smith

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 )

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