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 2006-01-03, 14:44 #133 Kosmaj     Nov 2003 2·1,811 Posts Found two for n=172: 8376860859765 172 9317981869455 172 (10000000000000) All prp's certified prime using Primo.
2006-01-04, 01:19   #134
Dougy

Aug 2004
Melbourne, Australia

9816 Posts

I've updated the list of known octoproths and verified that all of the listed octoproths with n>=100. I've gotten rid of the upper bound on k - it just seemed to be a bit pointless. An explaination of the notation used is now included, I hope it makes things clear.

Tell me if there's anything I've missed, or mistyped.

Edit: I just noticed I missed 9334074009855 143 smh (9334074009855)
Attached Files
 octoproth.txt (8.1 KB, 156 views)

Last fiddled with by Dougy on 2006-01-04 at 01:25

 2006-01-04, 12:49 #135 smh     "Sander" Oct 2002 52.345322,5.52471 29×41 Posts Thanks for the update. I've found octoproths for all N below 151 except for 146 and 149. I haven't done anything above 150. I'll post an update in a couple of days (or if i've found these last two earlier)
 2006-01-04, 17:13 #136 fetofs     Aug 2005 Brazil 2×181 Posts Status update I'd like to release n=151 at 600000000000. n=202 is at 1439553393195, sieving for more.
2006-01-04, 23:43   #137
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

2×733 Posts
fast octo program in GMP

Hi!

Some good news:
I've written a GMP program ( for linux ) to find octoproth primes. See my attachment for the c program. You can use it by ./a.out 50 1000000000 10000000000 if your program's name is a.out and you are searching for n=50, kmin=1000000000, kmax=10000000000. The sieving and prp testing are built in the program, so the output is the result ( these are prp primes for base 3).
Some of the part's of the code is commented but the main part and some tricks are not, sorry for this.

It is a really very fast program, it is faster than octo_fast if the range=kmax-kmin is large. ( for example if range>10^12 ) but it is very fast if range>1.94*10^12 (approx. 10^13). I've reached a speed up by a factor of 14 for large ranges. ( I think that in theory you can get also some extra speed up if range>4.47*10^14 ).

The program will find the octoproths in random order so the order is not increasing. This means that you have to search the full range, if you want to get the smallest solution for a certain n value.

Note that program's speed is very different for the same input numbers. I don't know why. I've gotten 83 and 213 sec. total time for the same numbers. Perhaps this is my computer's hardware problem.

The program print out the status ( this is an approximation ) and the exact time to follow the program's speed. I've also added that the results will be saved to results_octo.txt file. ( The searched range n,kmin,kmax, the found k,n values and the computation time ). But in this version you can't resume the work if you killed the program.

Can you verify my work and post some results using my program for large ranges?

Possibly somebody on this forum can make an exe file for windows users, I can't make this.
Attached Files
 octo.txt (8.6 KB, 117 views)

 2006-01-05, 10:14 #138 Kosmaj     Nov 2003 2×1,811 Posts Found the first octo for n=217 (possibly the largest so far?): 90817054219065 217 checked to 94.1T (9.41E13) using octo_fast. I'm now testing the new program by R. Gerbicz, will publish results shortly, it appears to be OK. Last fiddled with by Kosmaj on 2006-01-05 at 10:15
 2006-01-05, 10:49 #139 Greenbank     Jul 2005 2×193 Posts Nice work, I was doing something similar yesterday (porting the pascal code to GMP). By the way, endk can be bounded at 2^n if you rule out negative values. As k increases the first value to go negative will be 2^n-k.
2006-01-05, 12:21   #140
fetofs

Aug 2005
Brazil

2·181 Posts

Quote:
 Originally Posted by Kosmaj Found the first octo for n=217 (possibly the largest so far?): 90817054219065 217 checked to 94.1T (9.41E13) using octo_fast. I'm now testing the new program by R. Gerbicz, will publish results shortly, it appears to be OK.

Wow! Log10(90817054219065*2^217+1)=79.2816764699...
Definitely the largest so far...

By the way, gcc isn't compiling Gerbicz's program...

Code:
octo.c:7:26:sys/resource.h: No such file
octo.c: In function 'cputime':
octo.c:22: storage size of 'rus' isn't known

2006-01-05, 12:43   #141
TTn

Quote:
 Hi! Some good news: I've written a GMP program ( for linux ) to find octoproth primes. See my attachment for the c program. You can use it by ./a.out 50 1000000000 10000000000 if your program's name is a.out and you are searching for n=50, kmin=1000000000, kmax=10000000000. The sieving and prp testing are built in the program, so the output is the result ( these are prp primes for base 3). Some of the part's of the code is commented but the main part and some tricks are not, sorry for this. It is a really very fast program, it is faster than octo_fast if the range=kmax-kmin is large. ( for example if range>10^12 ) but it is very fast if range>1.94*10^12 (approx. 10^13). I've reached a speed up by a factor of 14 for large ranges. ( I think that in theory you can get also some extra speed up if range>4.47*10^14 ). The program will find the octoproths in random order so the order is not increasing. This means that you have to search the full range, if you want to get the smallest solution for a certain n value. Note that program's speed is very different for the same input numbers. I don't know why. I've gotten 83 and 213 sec. total time for the same numbers. Perhaps this is my computer's hardware problem. The program print out the status ( this is an approximation ) and the exact time to follow the program's speed. I've also added that the results will be saved to results_octo.txt file. ( The searched range n,kmin,kmax, the found k,n values and the computation time ). But in this version you can't resume the work if you killed the program. Can you verify my work and post some results using my program for large ranges? Possibly somebody on this forum can make an exe file for windows users, I can't make this.
I am still interested in doing this.
Since all octos are 15k, it will be a pleasing addition to the RMA group.
So I will have to modify it onto the .NET framework.
It could take awhile, since I'm not an expert at this.

Where is the file?
I'll need the source too, for translation.

2006-01-05, 13:01   #142
Kosmaj

Nov 2003

2×1,811 Posts

I compiled it under cygwin, try adding "-I/usr/include" or specify another folder where you have your header files.

I'm enclosing results. I did
n=52 to k=1T, found 90 octo's, only 4 were known before
n=97, to 12T, confirmed all to 10T and found 4 new ones in the 10-12T
n=151, to 12T
n=152, to 11T
n=154, to 10T, nothing found for these 3 n's.

Based on results for n=52 and n=97 it seems that the program is correctly finding all octos in the given range. I haven't done any comparison with octo_fast.

ps. I sorted the output for n=52, and I confirmed that all 90x8 numbers are pseudoprimes using Pari/GP. The output for n=97 is exactly as written by the program.
Attached Files
 results_octo.txt (2.7 KB, 94 views)

2006-01-05, 13:04   #143
Greenbank

Jul 2005

2·193 Posts

Quote:
 Originally Posted by TTn I am still interested in doing this. Since all octos are 15k, it will be a pleasing addition to the RMA group. So I will have to modify it onto the .NET framework. It could take awhile, since I'm not an expert at this. Where is the file? I'll need the source too, for translation. Include any comments if possible.
The source file is provided in his post as the "octo.txt" attachment.

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