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 smh 2005-04-18 15:45

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)[/CODE]

I'll try 135 next

 axn 2005-04-18 15:52

[QUOTE=smh]I'll try 135 next[/QUOTE]

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.

 Templus 2005-04-18 16:41

[QUOTE=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[/QUOTE]

I am terribly sorry, I forgot to extend the ABC-line :redface: :redface:
I will test k=235 further on!

 smh 2005-04-18 19:32

[QUOTE=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.[/QUOTE]

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

 Dougy 2005-04-18 23:31

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. :showoff:

Secondly, both bases 32 and 33 have no octoproth primes. :sad:

 Dougy 2005-04-19 02:21

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... :sad: But fortunately I kept the sieved files.

URL: [url]http://www.alpertron.com.ar/ECM.HTM[/url]

 axn 2005-04-19 03:56

[QUOTE=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... :sad: But fortunately I kept the sieved files.

URL: [url]http://www.alpertron.com.ar/ECM.HTM[/url][/QUOTE]

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!

 Dougy 2005-04-19 06:16

Interesting things...

1 Attachment(s)
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 :exclaim: 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,...

 axn 2005-04-19 08:12

[QUOTE=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 :exclaim: 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,...[/QUOTE]

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[/code]

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 :smile:

 Dougy 2005-04-19 10:09

Wow lots of holes.

1 Attachment(s)
Wow thanks, I didn't think there could be so many missing... it's all updated now. :smile:

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

Most Wanted: n=72... searched k<1000000000000. :question:

 smh 2005-04-19 20:09

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)[/CODE]

:banana: :bounce: :banana:

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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