- **Octoproth Search**
(*https://www.mersenneforum.org/forumdisplay.php?f=63*)

- - **Octoproths**
(*https://www.mersenneforum.org/showthread.php?t=3956*)

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 |

[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. |

[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! |

[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 |

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: |

Hmmm a bug in Dario Alpern's ECMWhen 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=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! |

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,... |

[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: |

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: |

142I'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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