20060103, 14:44  #133 
Nov 2003
2·1,811 Posts 
Found two for n=172:
8376860859765 172 9317981869455 172 (10000000000000) All prp's certified prime using Primo. 
20060104, 01:19  #134 
Aug 2004
Melbourne, Australia
98_{16} 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) Last fiddled with by Dougy on 20060104 at 01:25 
20060104, 12:49  #135 
"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) 
20060104, 17:13  #136 
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. 
20060104, 23:43  #137 
"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=kmaxkmin 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. 
20060105, 10:14  #138 
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 20060105 at 10:15 
20060105, 10:49  #139 
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^nk. 
20060105, 12:21  #140  
Aug 2005
Brazil
2·181 Posts 
Quote:
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 

20060105, 12:43  #141  
ADD_{16} Posts 
Quote:
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. 

20060105, 13:01  #142 
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 1012T 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. 
20060105, 13:04  #143  
Jul 2005
2·193 Posts 
Quote:


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