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

 MyDogBuster 2009-12-22 22:26

Riesel Base 529

Riesel 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

 MyDogBuster 2009-12-22 22:35

Riesel Base 676

Riesel 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

 MyDogBuster 2009-12-22 22:38

Riesel Base 729

Riesel 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

 MyDogBuster 2009-12-26 16:41

Riesel Base 784

Riesel 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

 MyDogBuster 2009-12-26 16:49

Riesel Base 900

Riesel 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

 henryzz 2009-12-29 18:12

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

 gd_barnes 2009-12-30 05:15

[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.

 MyDogBuster 2009-12-30 05:59

[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.

 henryzz 2009-12-30 10:59

[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

 rogue 2009-12-31 14:37

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.

 kar_bon 2010-01-02 00:59

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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