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

- - **Bases 501-1030 reservations/statuses/primes**
(*https://www.mersenneforum.org/showthread.php?t=12994*)

Riesel Base 529Riesel Base 529
Conjectured k = 54 Covering Set = 5, 53 Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 11(11) Found Primes: 15k's File attached Remaining k's: 36*529^n-1 <----- Proven composite by full algebraic factors Trivial Factor Eliminations: 10k's Conjecture Proven HTML attached |

Riesel Base 676Riesel Base 676
Conjectured k = 149 Covering Set = 7, 31, 37 Trivial Factors k == 1 mod 3(3) and k == 1 mod 5(5) Found Primes: 76k's File attached Remaining k's: Tested to n=25K 9*676^n-1 <----- Proven composite by full algebraic factors 144*676^n-1 <----- Proven composite by full algebraic factors Trivial Factor Eliminations: 69k's Conjecture Proven HTML attached |

Riesel Base 729Riesel Base 729
Conjectured k = 74 Covering Set = 5,73 Trivial Factors k == 1 mod 2(2) and 1 mod 7(7) and 1 mod 13(13) Found Primes: 25k's File attached Remaining k's: Tested to n=25K 4*729^n-1 <----------- Removed due to full algebraic factors 16*729^n-1 <----------- Removed due to full algebraic factors 24*729^n-1 Trivial Factor Eliminations: 8 14 22 36 40 50 64 66 Base Released HTML attached |

Riesel Base 784Riesel Base 784
Conjectured k = 156 Covering Set = 5, 157 Trivial Factors k == 1 mod 3(3) and k == 1 mod 29(29) Found Primes: 93k's File attached Remaining k's: Tested to n=25K 9*784^n-1 <----- Proven composite by full algebraic factors 36*784^n-1 <----- Proven composite by full algebraic factors 69*784^n-1 81*784^n-1 <----- Proven composite by full algebraic factors 116*784^n-1 144*784^n-1 <----- Proven composite by full algebraic factors Trivial Factor Eliminations: 55k's Base Released HTML attached |

Riesel Base 900Riesel Base 900
Conjectured k = 52 Covering Set = 17, 53 Trivial Factors k == 1 mod 29(29) and k == 1 mod 31(31) Found Primes: 41k's File attached Remaining k's: Tested to n=25K 4*900^n-1 <----- Proven composite by full algebraic factors 9*900^n-1 <----- Proven composite by full algebraic factors 16*900^n-1 <----- Proven composite by full algebraic factors 22*900^n-1 25*900^n-1 <----- Proven composite by full algebraic factors 36*900^n-1 <----- Proven composite by full algebraic factors 49*900^n-1 <----- Proven composite by full algebraic factors Trivial Factor Eliminations: 30 32 Base Released HTML attached |

i have had 2 more primes since n=3k
744*589^4026+-1 654*589^5638+-1 i am now tested upto n=20k this lack of recent primes is getting frustrating |

[quote=henryzz;200227]i have had 2 more primes since n=3k
744*589^4026+-1 654*589^5638+-1 i am now tested upto n=20k this lack of recent primes is getting frustrating[/quote] I don't blame you for being annoyed. If there's one thing I've personally found with the very large bases, it's that you can go into extremely long stretches of no primes after a large grouping of primes. I'm sure Ian can relate the same experience. |

[QUOTE] I'm sure Ian can relate the same experience. [/QUOTE]
Yup, the galactic voids are all over the place. I guess this is part of the exercise. Not only can a pattern of primes be found (hopefully) but also a pattern of voids would also be useful. |

[quote=gd_barnes;200281]I don't blame you for being annoyed. If there's one thing I've personally found with the very large bases, it's that you can go into extremely long stretches of no primes after a large grouping of primes. I'm sure Ian can relate the same experience.[/quote]
i worked out the probability using your odds or prime spreadsheet and i should have found 1.2 primes in the range 5k-10k and also 1.2 primes in the range 10k-20k this was based on data after the primes just mentioned i found the prime for 5k-10 before the analysis but am still owed the prime for 10k-20k i suppose i was being lucky before cant wait for finding another prime |

Riesel base 707 proven with prime:
12*707^10572-1 No, I did not reserve it. I just took a bunch of bases that had a few k left where n < 25000 and are taking them to n = 25000 as part of my testing for the upcoming PRPNet release. I will avoid stepping on toes by not posting primes for bases reserved by others. |

Riesel base 1019:
the only k=2 is at n=91k (so about n=910k for base 2) no prime yet. continuing. |

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