- **Conjectures 'R Us**
(*https://www.mersenneforum.org/forumdisplay.php?f=81*)

- - **Bases 33-100 reservations/statuses/primes**
(*https://www.mersenneforum.org/showthread.php?t=10475*)

Bases 33-100 reservations/statuses/primes1 Attachment(s)
Admin. edit: We have started this new thread for bases 33-100. See more info. in [URL="http://www.mersenneforum.org/showpost.php?p=137717&postcount=14"]post 11[/URL] of the effort here.
[quote=gd_barnes;137054] I hope that no new bases are started for the next several months now! :smile: Gary[/quote] I have already finished this one. Willem. |

bases 33-100[quote=Siemelink;137058]I have already finished this one.
Willem.[/quote] Willem, I forgot to mention here when I checked this a week ago: Nice work on proving the Riesel base 33 conjecture at k=764. All k-values were accounted for with 2 of them having algebraic factors. The proof was added to the web pages after I checked it. To all: If you want to tackle a base or two higher than 32, that's fine as long as the conjecture is low; preferrably < ~2500. Most low conjectures are easy to administer and check. You'll have to determine what the lowest Riesel or Sierp value is with a covering set. There's a thread that talks about software that can do this. In the past, I've used a crude method that uses srsieve sieving software that is quite accurate for determining low conjectures but it's a little combersome to set up and use. Before starting on a base, please let us know that you are reserving it, what the conjectured value is, and what the covering set is. Gary |

[QUOTE=gd_barnes;137693]Before starting on a base, please let us know that you are reserving it, what the conjectured value is, and what the covering set is.
Gary[/QUOTE] Ah yes, other bases. I wrote a program to calculate conjectures myself. I've also done some more work on the Riesel bases until 50. Bases 34, 38, 41, 43, 44, 47 and 50 are trivial to prove. Bases 35, 39, and 40 have conjectures higher than a million. Bases 36, 37, 42, 45, 46, 48 have between 20 and 100 remaining k at n = 10,000 Base 49 has 1 remaining k. That one I'd like reserved for myself. Gary, I hadn't mentioned this because I did't want to hand over the data to you and dropping you in a hole like I did with the base 25. I'll post the trivial conjectures when I have them in the same format as the one that I gave last week. As for the others, tell me how you like the data and I'll format it that way. Willem. |

base 34Base 34 has riesel = 6.
If (k mod 3) == 1 then for any n there is a factor 3. This eliminates k = 1 and k = 4. k n 2 1 3 1 5 2 6 Riesel covering set {5, 7} odd n: 7 even n: 5 |

base 38Base 38 has Riesel = 13
Covering set {3. 5. 17} k n 1 1 2 2 3 1 4 1 5 2 6 1 7 7 8 2 9 43 10 1 11 766 12 2 13 Riesel Listed by decreasing n: k n 11 766 9 43 7 7 5 2 2 2 12 2 8 2 3 1 1 1 6 1 10 1 4 1 |

Base 41Base 41 has Riesel = 8
If k is odd then any n will have a factor 2. This eliminates k = 1, 3, ,5 , 7. If (k mod 5) == 1 then any n will have a factor 5. This eliminates k = 6. k n 2 2 4 1 8 Riesel Covering set {3, 7} |

base 431 Attachment(s)
Base 43 has Riesel = 672
covering set = {5, 11, 37} Excluded: k mod 2 = 1 k mod 3 = 1 k mod 7 = 1 highest primes 308 624 12 203 516 202 450 162 494 148 476 101 104 77 560 70 384 48 188 37 All primes in attachment. |

base 44Base 44 hase Riesel = 4
Covering set = {3, 5} Primes k n 1 1 2 4 3 1 |

base 47Base 47 has Riesel = 14
Covering set = {3, 5 ,13} excluded: odd k k n 2 4 4 1555 6 1 8 32 10 51 12 1 |

base 50Base 50 has riesel = 16
covering set = {3, 17} (k mod 7) == 1 has factor 7. This eliminates 1, 8 and 15 k n 2 2 3 1 4 1 5 12 6 6 7 1 9 1 10 1 11 6 12 1 13 19 14 66 Listed by decreasing n: 14 66 13 19 5 12 11 6 6 6 2 2 12 1 4 1 3 1 9 1 10 1 7 1 |

Bases 33-100 reservations/statusesReport all reservations/status for bases 33-100 in this thread.
These would be low priority and something to be worked on 'just for fun' that are not too CPU-intensive. It is preferred that you only stick with low-conjectured bases; preferrably with a conjecture of k<2500. Before starting on a base, please state that you are reserving it, its conjectured value, and the covering set. Please post all primes, statuses, and results in this thread. When reporting things, please account for all k-values in some manner. This will help keep the admin. effort to a minimum. :smile: Gary |

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