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 2005-04-18, 15:45 #67 smh     "Sander" Oct 2002 52.345322,5.52471 29·41 Posts I tested n=141 with the old executable upto k=5,555*10^13 This is the closest i got: Code: 43354856050725*2^141+1 is 3-PRP! (0.0004s+0.0004s) 43354856050725*2^141-1 is 3-PRP! (0.0002s+0.0038s) 43354856050725*2^(141+1)+1 is 3-PRP! (0.0002s+0.0022s) 43354856050725*2^(141+1)-1 is 3-PRP! (0.0002s+0.0021s) 2^141+43354856050725 is 3-PRP! (0.0001s+0.0021s) 2^141-43354856050725 is 3-PRP! (0.0001s+0.0030s) 2^(141+1)+43354856050725 is 3-PRP! (0.0001s+0.0023s) 2^(141+1)-43354856050725 is composite: [2FAAB440A92EB3DC] (0.0001s+0.0022s) I'll try 135 next
2005-04-18, 15:52   #68
axn

Jun 2003

543610 Posts

Quote:
 Originally Posted by smh I'll try 135 next
If you are searching higher n's, try to search n = 4,7, or 10 (mod 15), esp n = 7 (mod 15). These are heavy weight n's. I think n=142 will make a good candidate.

2005-04-18, 16:41   #69
Templus

Jun 2004

2×53 Posts

Quote:
 Originally Posted by axn1 They differ only in the depth of the sieve, ie, the number of p's used to sieve. p < 10^5, 10^6 and 10^7 (resp. for fast, med & deep). PS:- The numbers you posted are not octos. They are only prime for 2^n+/-k and 2^(n+1)+/-k. They are not prime for the other forms, k*2^n+/-1 and k*2^(n+1)+/-1
I am terribly sorry, I forgot to extend the ABC-line
I will test k=235 further on!

2005-04-18, 19:32   #70
smh

"Sander"
Oct 2002
52.345322,5.52471

118910 Posts

Quote:
 Originally Posted by axn1 If you are searching higher n's, try to search n = 4,7, or 10 (mod 15), esp n = 7 (mod 15). These are heavy weight n's. I think n=142 will make a good candidate.

Okay, i'll test 142 then. I'm running the 'sieve' for a day or so on a p3 700 and see what pops up.

For 135 i didn't find any upto 1.196*10^13

12 had primes for the first 6 forms, of which 2 had also primes for the 7th form

 2005-04-18, 23:31 #71 Dougy     Aug 2004 Melbourne, Australia 23·19 Posts Wow 37!! So far every test I have put the new program through was passed. So I believe it is working fine. I ran the complete test on bases upto n=37. (and still going). And that base produced a whopping 83 octoproth primes. Secondly, both bases 32 and 33 have no octoproth primes. Last fiddled with by Dougy on 2005-04-18 at 23:32
 2005-04-19, 02:21 #72 Dougy     Aug 2004 Melbourne, Australia 23×19 Posts Hmmm a bug in Dario Alpern's ECM When I put these (and others) into the batch factorisation: 2^39-540206575755 2^39-539552526135 and test for primality it says (even if i just type in the decimal too!) 9549238133 is composite 10203287753 is composite However if I factorize them instead 9549238133 = 9549238133 10203287753 = 10203287753 implying they're prime. This means that I will have missed some octoproths... But fortunately I kept the sieved files. URL: http://www.alpertron.com.ar/ECM.HTM
2005-04-19, 03:56   #73
axn

Jun 2003

22·32·151 Posts

Quote:
 Originally Posted by Dougy When I put these (and others) into the batch factorisation: 2^39-540206575755 2^39-539552526135 and test for primality it says (even if i just type in the decimal too!) 9549238133 is composite 10203287753 is composite However if I factorize them instead 9549238133 = 9549238133 10203287753 = 10203287753 implying they're prime. This means that I will have missed some octoproths... But fortunately I kept the sieved files. URL: http://www.alpertron.com.ar/ECM.HTM
I too ran into this problem yesterday, while working with one of the lower n's (32, I think).

The "deep" version sieves upto p < 10^7, which means that for n <= 45 all the candidates will be automatically prime for 2^n+/-k forms!

You definitely need to recheck base 32 and 33!

Last fiddled with by axn on 2005-04-19 at 03:57

2005-04-19, 06:16   #74
Dougy

Aug 2004
Melbourne, Australia

2308 Posts
Interesting things...

After rechecking the small bases, I've updated the text file again. It should be fixed. I've completed upto n=41. Some interesting properties...

Number of octoproth-primes for n=27,28,29,...
1,2,1,1,2,0,0,7,17,11,90,28,83,331,109,...

n=40 alone has 331 octoproth-primes To think only the other day I was hoping to break the 100 mark.

Number of k-values unsieved (octo_deep) for n=27,28,29,... over all possible k-values.
2,4,4,2,19,22,13,110,137,85,802,360,844,4434,1651,7552,...
Attached Files
 octoproth.txt (22.5 KB, 184 views)

2005-04-19, 08:12   #75
axn

Jun 2003

10101001111002 Posts

Quote:
 Originally Posted by Dougy After rechecking the small bases, I've updated the text file again. It should be fixed. I've completed upto n=41. Some interesting properties... Number of octoproth-primes for n=27,28,29,... 1,2,1,1,2,0,0,7,17,11,90,28,83,331,109,... n=40 alone has 331 octoproth-primes To think only the other day I was hoping to break the 100 mark. Number of k-values unsieved (octo_deep) for n=27,28,29,... over all possible k-values. 2,4,4,2,19,22,13,110,137,85,802,360,844,4434,1651,7552,...
Some missing values for n=32,33,34,35, and 37.

Code:
n = 32
---------
409668105
664495755
2368386195
2709707805
3383804865
3692088225
3762658725

n = 33
---------
715414875
6876947175

n = 34
---------
293705775
1183281975
1397861655
3767954715
4597935705
8596001505

n=35
---------
17182250085
17783238795
20646922695
21811399155
22622064465
23416146075
24115395465
24449183535
25380028905

n=37
-----------
7218568995
126139443165
n = 36,38,39, and 40 are fine.

Also, I have checked all high k's for n =27 thru 64 (high k's are k's that can't be reliably sieved because 2^n-k becomes smaller than the largest sieve prime). There are no hidden octo's in there

2005-04-19, 10:09   #76
Dougy

Aug 2004
Melbourne, Australia

100110002 Posts
Wow lots of holes.

Wow thanks, I didn't think there could be so many missing... it's all updated now.

So there might be octo's for all bases after 27. I've added the smallest octo for each base upto 71.

Most Wanted: n=72... searched k<1000000000000.
Attached Files
 octoproth.txt (23.7 KB, 251 views)

 2005-04-19, 20:09 #77 smh     "Sander" Oct 2002 52.345322,5.52471 29·41 Posts 142 I've found the following for n=142, searching K from 1 to 3.09x10^13 Code: 8444737373415*2^142+1 is 3-PRP! (0.0002s+0.0002s) 8444737373415*2^142-1 is 3-PRP! (0.0002s+0.0023s) 8444737373415*2^(142+1)+1 is 3-PRP! (0.0002s+0.0023s) 8444737373415*2^(142+1)-1 is 3-PRP! (0.0018s+0.0023s) 2^142+8444737373415 is 3-PRP! (0.0001s+0.0024s) 2^142-8444737373415 is 3-PRP! (0.0001s+0.0023s) 2^(142+1)+8444737373415 is 3-PRP! (0.0001s+0.0023s) 2^(142+1)-8444737373415 is 3-PRP! (0.0001s+0.0024s) 9532236817845*2^142+1 is 3-PRP! (0.0002s+0.0029s) 9532236817845*2^142-1 is 3-PRP! (0.0002s+0.0024s) 9532236817845*2^(142+1)+1 is 3-PRP! (0.0002s+0.0024s) 9532236817845*2^(142+1)-1 is 3-PRP! (0.0002s+0.0025s) 2^142+9532236817845 is 3-PRP! (0.0001s+0.0023s) 2^142-9532236817845 is 3-PRP! (0.0001s+0.0023s) 2^(142+1)+9532236817845 is 3-PRP! (0.0001s+0.0023s) 2^(142+1)-9532236817845 is 3-PRP! (0.0001s+0.0026s) 22732824274545*2^142+1 is 3-PRP! (0.0002s+0.0003s) 22732824274545*2^142-1 is 3-PRP! (0.0002s+0.0024s) 22732824274545*2^(142+1)+1 is 3-PRP! (0.0002s+0.0024s) 22732824274545*2^(142+1)-1 is 3-PRP! (0.0002s+0.0024s) 2^142+22732824274545 is 3-PRP! (0.0001s+0.0023s) 2^142-22732824274545 is 3-PRP! (0.0001s+0.0023s) 2^(142+1)+22732824274545 is 3-PRP! (0.0001s+0.0024s) 2^(142+1)-22732824274545 is 3-PRP! (0.0001s+0.0024s) Close to 2 million numbers survived the sieve. Newpgen didn't make sence after this, since it removed candidates much slower than i was able to prp them. I'll try 157 (another 7 mod 15) next.

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