20060113, 20:23  #254  
"Sander"
Oct 2002
52.345322,5.52471
29×41 Posts 
Quote:


20060114, 21:16  #255 
"Robert Gerbicz"
Oct 2005
Hungary
5FB_{16} Posts 
"Small project"
I would like to propose a "small project":
take my octo_4_5 program, only the sieving part from c to assembly ( in sieving part don't replace gmp instructions by assembly ), because prp checking is in Gmp and that is quite efficient. Note that I've never written assembly program. I think it isn't very hard, see my code there is only such an instructions like: for, while, if, else , , ++, , + There is only one modular multiplication per sieving prime. It's cost isn't large, but put this also to assembly, if you can do. I think we can gain about 10%20% speed up only, because most of the instructions is only addition and I've highly unrolled the for cycle also in a cache friendly way: see b[j]=0,b[j+A1]=0,b[j+A2]=0,b[j+A3]=0,b[j+A4]=0,b[j+A5]=0,b[j+A6]=0,b[j+A7]=0; Ps. I don't see any further improvement in the sieving code, it is very optimized in c, put it to assembly. This octo program is the fastest program that I've ever written in c. Perhaps I'll rewrite some part of the prp checking code. Last fiddled with by R. Gerbicz on 20060114 at 21:22 
20060115, 23:16  #256 
"Robert Gerbicz"
Oct 2005
Hungary
1,531 Posts 
octo_5_0 program
Returning to octo program:
I've implemented the tricks, what I've used for dodeca program. On some very critical ranges it is faster by about 5% than previous version. Now you can type: ( use big T ) octo_5_0 150 42T 647T if you want to search n=150 from 42*10^12 to 647*10^12 Note that you can type also octo_5_0 150 42000000000000 647000000000000 and note if you type decimals that are not divisible by 10^12, then I redefine these: rounding down for kmin and rounding up for kmax, so these will be divisible by 10^12. So if you type: octo_5_0 150 42760000000000 169120000000000 Then after redefinition you will get on the screen: n=150, kmin=42T, kmax=170T, version=5.0, here T=10^12 It won't increase the time because it means that you'll search maximum a 2T larger interval, but this is very easy for octo program. I hope this is clear for everybody, but you can ask. You can download exe from: http://www.robertgerbicz.tar.hu/octo_5_0.exe or see the attachment for the c code. Ps. Thanks for Greenbank, I've mainly implemented his string program! 
20060116, 11:20  #257 
Jul 2005
2×193 Posts 
All Dodecaproth discussions moved to a new thread:
http://www.mersenneforum.org/showthread.php?t=5358 This thread remains for further discussion on Octoproths. 
20060116, 19:29  #258 
Jun 2003
Oxford, UK
11111100001_{2} Posts 
Latest Executables
Can we move Robert G's latest executables to a new thread?
Regards Robert Smith 
20060116, 20:31  #259 
Jun 2003
Oxford, UK
2,017 Posts 
Aiaia
Sorry guys, should have checked "how to help" first. Ignore this and last post.
Regards Robert Smith 
20060117, 12:17  #260 
"Robert Gerbicz"
Oct 2005
Hungary
1,531 Posts 
The smallest octoproth for a given n
I've posted in the octoproth reservation thread that the smallest k value is about 2^n/f(n) Looking the tables in almost every cases the smallest k value is smaller than this prediction. It's a little overestimation, I'll think about it what would be a better estimation. The problem is that if k is small than all 8 eight numbers are also small, so they have got a higher probability that they are primes.

20060117, 19:15  #261 
"Robert Gerbicz"
Oct 2005
Hungary
1,531 Posts 
Weight of n ( for octoproths ) ( PARI programs )
Code:
w(n)=T=128.0;forprime(p=3,10^4,l=listcreate(8);g=Mod(2,p)^n;h=1/g;\ a=[g,g,h,h,2*g,2*g,h/2,h/2];a=lift(a);for(i=1,8,listput(l,a[i],i));\ l=listsort(l,1);T*=(1length(l)/p)/(11/p)^8);return(T) Code:
f(n)=round(w(n)*2^n/(n*log(2))^8*1/16) much smaller or larger, this is only an "average" expected k value: ( new estimation! ) Code:
s(n)=d=0.0;c=w(n)/(n*log(2))^8;forstep(i=1.0/2^15,1.0,1.0/2^15,\ d+=c*(2^(i*n)2^((i1/2^15)*n))/(1+i)^4;if(d>1.0,return(round(2^(i*n)))));return Last fiddled with by R. Gerbicz on 20060117 at 19:21 
20060119, 11:53  #262 
Jul 2005
2·193 Posts 
Nice work Robert.
When I get a chance I'll compute your estimations for all n < 500 (if PARI allows this, I know a previous version stopped working around n=140 due to precision limitations). We can then see how these compare to the number of Octoproths found for the completed ranges. I've also finished n=55 and I'm just running all of them through PARI to confirm they are all primes. When I have the final number I'll update it. n=56 is 50% of the way through, only running on one CPU though so it will take another 1.5 days. I doubt I'll go as far as n=57. When I start throwing the data into mysql on my website I can also have a page showing lowest k per n, and the estimate that your formula produces. We can see how accurate it is then :) I know I'm constantly saying "when the website appears" but I am working on it, just taking longer than I expected plus I had to redesign lots of bits when the idea of Dodecaproths (and hexadeca, icosa, etc) came along. 
20060119, 12:44  #263 
Jul 2005
2×193 Posts 
n=55 results in "Number of Octoproths per n" thread.
Here are the other bits of results_octo.txt (without the 700,000 Octoproths!): n=55, kmin=0T, kmax=10000T, version=5.0, here T=10^12 Starting the sieve... Using the first 10 primes to reduce the size of the sieve array The sieving is complete. Number of Prp tests=1014929270 Time=132475 sec. n=55, kmin=10000T, kmax=20000T, version=5.0, here T=10^12 Starting the sieve... Using the first 10 primes to reduce the size of the sieve array The sieving is complete. Number of Prp tests=1012619035 Time=132608 sec. n=55, kmin=20000T, kmax=30000T, version=5.0, here T=10^12 Starting the sieve... Using the first 10 primes to reduce the size of the sieve array The sieving is complete. Number of Prp tests=1012427473 Time=136325 sec. n=55, kmin=30000T, kmax=36030T, version=5.0, here T=10^12 Starting the sieve... Using the first 10 primes to reduce the size of the sieve array The sieving is complete. Number of Prp tests=614381871 Time=81683 sec. Total PRP tests: 3654357649 Total time taken: 483091 (5 days 14 hours 11 mins 31 secs). 
20060119, 12:59  #264  
"Robert Gerbicz"
Oct 2005
Hungary
1,531 Posts 
Quote:
See for example: (13:52) gp > \p 100 realprecision = 105 significant digits (100 digits displayed) (13:52) gp > Don't choose very large precision, because it would slow down the whole computation. 

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