Riesel/Sierp #'s for bases 3, 7, and 15

[michaf]

Originally Posted by gd_barnes

There is one more thing I'd like to bring up here. I would prefer if we avoided continuing to start on new bases. Could we please hold off on k=7 and 15 for now? It is a very large administrative effort on my/our part here each time a new base is started, especially on bases with large conjectures or that are not very prime bases...recent examples are bases 3 and 19. Also, I haven't even had a chance to review the new base 25 work done by Siemlink, which has many primes from base 5 that can be used to eliminate some k-values. The effort it takes to verify and make sure everything is as correct as possible is very large for such bases. Even on a lesser base, Riesel base 24, it took several hours to come up with the correct algebraic factors for it that effectively eliminated 26 k-values in order to avoid future unnecessary work.

Gary, I have absolutely NO intentions on starting on either of those bases, it was just plain curiosity if they were also 'very prime'. (And for bases >31, I didn't know such a list existed, and was just curious)

So, sit back and take a deep breath...

[Siemelink]

my program isn't finished yet. I am planning to include a base range as well. But first I want it quicker....

Willem.

[gd_barnes]

Originally Posted by michaf

Gary, I have absolutely NO intentions on starting on either of those bases, it was just plain curiosity if they were also 'very prime'. (And for bases >31, I didn't know such a list existed, and was just curious)

So, sit back and take a deep breath...

AHHHHHHHHHHHHHHHH!!!!!!!

I can feel the fresh ocean breeze as I sit back and take in its relaxing aroma amid the lack of new bases started.

[robert44444uk]

Originally Posted by michaf

And for bases >31, I didn't know such a list existed, and was just curious

I looked at a variety of bases originally that might not provide terribly convenient covering sets - but it should be easy to conclude that for all bases above a specific and small integer, that a maximum of 12-cover exist for all values, and in many cases this is 2,3,4 or 6-cover:

Factor b^1-1 and the prime factors provide values that are not useful for covering sets.

Factor b^12-1 and find five new prime factors - because each of b^2-1, b^3-1, b^4-1 and b^6-1 introduces one new prime factor, (with b<>2^i-1 where i is an integer), and these factors provide at maximum 12-cover.

Looking at b=2^i-1, i integer, therefore, is the remaining interesting area for covering sets, as b^2-1 does not provide extra prime factors.

I think the smallest covering sets for the first few values of i are as follows:

i b=2^i-1 smallest cover

3 7 24
4 15 24?
5 31 12
6 63 12
7 127 6
8 255 6
9 511 24
10 1023 3
11 2047 6
12 4095 6
13 8191 12
14 16383 3
15 32767 12
16 65535 12
17 131071 3
18 262143 6
19 524287 6
20 1048575 4
21 2097151 6
22 4194303 3
23 8388607 4
24 16777215 6

I wonder if b=511 is the largest base with cover greater than 12?

For non b=2^i-1, as b gets larger it is really hard to find values where the smallest cover set is 12, as b^3-1, b^4-1, b^6-1 must only produce 1 new prime at each step up. An example is b=47110, with new primes introduced at

n new prime factor
1 3,41,383
2 47111
3 739799737
4 2219352101
6 2219304991

[tnerual]

Originally Posted by robert44444uk

Robert

I am having problems running the covering.exe program

I type in the command such as: D:\ covering 4 8 1 100 100000000 and get no response, just a move of the cursor to the next line. Looking at tneural's output makes me think that you programme is supposed to respond with some screen outputs, but I get nothing. And the CPU does not appear to be used, which means I am doing something fundamentally wrong.

I am using an AMD ML 40.

Maybe it is not supposed to work on this type of machine.

the command you use is not working

i use this:

covering  [ENTER]
exponent [ENTER]
base [ENTER]
riesle/sierp [ENTER]
prime range [ENTER]
best vaue found [ENTER]

after the 6th [ENTER], the program start ...

it's a lot of manual work, but i had time to try up to 431 (432 running at the moment) no better results at the moment !

[michaf]

For me worked:

covering (enter)
4 8 1 100 100000000 (enter)

program works...
program ends...

arrow up (enter) (this gives again covering
arrow up (this gives the same input, you only need to change the exponent)

[gd_barnes]

Originally Posted by michaf

For me worked:

covering (enter)
4 8 1 100 100000000 (enter)

program works...
program ends...

arrow up (enter) (this gives again covering
arrow up (this gives the same input, you only need to change the exponent)

Is there a way to turn this into a batch process? I tried this in a file I called batch.bat:
covering
4 8 -1 10000 1000000
covering
6 8 -1 10000 1000000
.
.
.
(etc.)

I then typed 'batch' at the command line and it executed the 'covering' program but it then waits for input from me. That is it won't get the input from the 2nd line.

Is there a way to tell it to accept the input from the 2nd line? I also tried "covering 4 8 -1 10000 1000000" all on each line of the batch file, the same as what Robert used at the command line for a non-batch process, and had the same problem that he did. It just ignores the rest of the line after the 'covering' command.


On another note, here are a couple of enhancements that I might suggest (if not already suggested):

Allow a range of exponents to be entered and write the output to a file. Perhaps by a 6th input such as in:
4
144
8
-1
10000
1000000



So the above would test exponents 4 thru 144 and write the output to some .txt file.

Thanks for a great program!


Gary

[mdettweiler]

Originally Posted by gd_barnes

Is there a way to turn this into a batch process? I tried this in a file I called batch.bat:
covering
4 8 -1 10000 1000000
covering
6 8 -1 10000 1000000
.
.
.
(etc.)

I then typed 'batch' at the command line and it executed the 'covering' program but it then waits for input from me. That is it won't get the input from the 2nd line.

Is there a way to tell it to accept the input from the 2nd line? I also tried "covering 4 8 -1 10000 1000000" all on each line of the batch file, the same as what Robert used at the command line for a non-batch process, and had the same problem that he did. It just ignores the rest of the line after the 'covering' command.

Try this:

echo 4 8 -1 10000 1000000 | covering
echo 6 8 -1 10000 1000000 | covering

...and etc. for the rest of the commands in the batch file.

[rogue]

Change the first few lines of the main() function to this:

int main(int argc, char *argv[])
{

    int N,b,C,v[32],w[32],A[32],L,LC,limit,temp,i,j,p,add,len;
    int pos,test,res,ord,all,p2,possible,e,*S,*R,**RES,**RES2,stored_LC[32];
    long long int best;
    long long int alpha,alpha2,beta,M,K,E;
    char word[32];

    if (argc == 6)
    {
       N = atol(argv[1]);
       b = atol(argv[2]);
       C = atol(argv[3]);
       limit = atol(argv[4]);
       strcpy(word, argv[5]);
    }
    else
       scanf("%d%d%d%d%s",&N,&b,&C,&limit,word);

then it will take arguments from the command line.

I suspect that using the FPU for the numerous mods in the code could double performance.

[robert44444uk]

Originally Posted by Anonymous

Try this:

echo 4 8 -1 10000 1000000 | covering
echo 6 8 -1 10000 1000000 | covering

...and etc. for the rest of the commands in the batch file.

Great, this works on my AMD. Happy puppy now

Astonishing software!!!!!

[KEP]

@ Everyone: Really great work you all do here. I can tell you, that if really wanna work on a huge base please consider run k-ranges above 500M k for base 3 riesel. If you use Michafs program, it will bring you fast in progress. However for the next month or so, no k above 500,000,000 for riesel base 3 will be worked at. So if you take any of the work above that k-range please just drop a note here, and I'll catch it before starting the next ranges.

On a sidenote, it takes ~315 MB of RAM to sieve 50,000 k's from n=1 to n=25,000 using srsieve.exe, but besides from that it causes no problems to run that many candidates and test them using srsieve.exe! Also on another note, due to memory issues, it is not recommended to use sr2sieve.exe since it requires about 700MB of RAM for every 1,500 k's. Whatever you decide any one of you, it really means a lot, of course if anyone brings the conjecture below k 500,000,000... well then please consider use your ressources somewhere else

Have a nice weekend, all of you, and Gary your very welcome, the least I could do was to send you the sieved files that I had, since no one really has to do more sieve when it was in fact at optimal depth at least for base 12 sierpinski. Good luck on finding a prime or at least take this big and huge leap in the Base 12 sierp testing, just hope you can do it without you or your computer gets hurt

Regards

KEP