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Bases 33-100 reservations/statuses/primes

1 Attachment(s)

[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.

 gd_barnes 2008-07-12 08:45

bases 33-100

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 34

Base 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 38

Base 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 41

Base 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 43

1 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 44

Base 44 hase Riesel = 4
Covering set = {3, 5}

Primes
k n
1 1
2 4
3 1

base 47

Base 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 50

Base 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

 gd_barnes 2008-07-12 19:42

Bases 33-100 reservations/statuses

Report 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.