Why Base 5 and Weights

[Citrix]

Originally Posted by Citrix

Robert,

It would be intresting to see if k's that are multiple of 3 or 5 or both can ever generate a sierpinski or riesel number for base 2? I will try to work on this later this week or as soon as I get some time and see what I can come up with. Base 5 takes too long as most of the optimizations for base 2 that make them super fast don't work for base 5. (I'm not sure if base 4 counts, but the smallest sierpinski number is k=5 for that base and I can prove that )

Citrix

I figured out how to generate sierpinski's that are multiples of 3 and 5 for base 2 but it is unlikely that any exist under 2^32, so it would not be feasible to work on that right now either. Base 5 seems the best search right now.


Citrix

[Citrix]

Robert, you can look at base 4 though.

66741 is the smallest sierpinski number for base 4 such that the k is always a multiple of 3 or k=3*h+1. where h is a natural number.

I have tested all the odd numbers, haven't had a chance to test the even k's yet. But there may be a smaller sierpinksi number for base 4.

So there will be fewer numbers k left and at the same time this is basically base 2 so will be 8 times faster than base 5.

I will do more testing on this tonight and post my results.

Citrix

[Citrix]

Originally Posted by Citrix

Robert, you can look at base 4 though.

66741 is the smallest sierpinski number for base 4 such that the k is always a multiple of 3 or k=3*h+1. where h is a natural number.

I have tested all the odd numbers, haven't had a chance to test the even k's yet. But there may be a smaller sierpinksi number for base 4.

So there will be fewer numbers k left and at the same time this is basically base 2 so will be 8 times faster than base 5.

I will do more testing on this tonight and post my results.

Only 37 k left so far. I will work more on this. K are going really fast. The lightest k has a weight of 181 so I should be able to solve this really soon.


Citrix

[siegert81]

How about a project in which base 3 is used, but instead of worrying about actually proving the S/R numbers in each case, the aim of the project would merely be to see how high of a "primeless" k value we can calculate?

So start with k=2,4,6,8... until the project gets "stuck" on a particular k value. Then, the n value would grow and grow until a prime is found for that k value, in which case the project would continue upwards to the next "difficult" k value.

In the process, the project would likely discover some large prime numbers, plus it could assert a minimum bound for the S/P numbers base 3, even if it never does prove either base 3 S/R conjecture.

Here, I'll start the project:

2*3^1+1=7 (prime!)
4*3^1+1=13 (prime!)
6*3^1+1=19 (prime!)
8*3^1+1=25=5*5

So I'm "stuck" on k=8. The exponent will have to be increased until a prime is found, in which case testing on k=10 may begin.

2*3^1-1=5 (prime!)
4*3^1-1=11 (prime!)
6*3^1-1=17 (prime!)
8*3^1-1=23 (prime!)
10*3^1-1=29 (prime!)
12*3^1-1=35=5*7

So I'm "stuck" on k=12. The exponent will have to be increased until a prime is found, in which case testing on k=14 may begin.

[Puzzle-Peter]

Originally Posted by siegert81

2*3^1+1=7 (prime!)
4*3^1+1=13 (prime!)
6*3^1+1=19 (prime!)
8*3^1+1=25=5*5

So I'm "stuck" on k=8. The exponent will have to be increased until a prime is found, in which case testing on k=10 may begin.

2*3^1-1=5 (prime!)
4*3^1-1=11 (prime!)
6*3^1-1=17 (prime!)
8*3^1-1=23 (prime!)
10*3^1-1=29 (prime!)
12*3^1-1=35=5*7

So I'm "stuck" on k=12. The exponent will have to be increased until a prime is found, in which case testing on k=14 may begin.

At the moment, the Riesel side is "stuck" at k=3677878, n=1000000. The Sierpinski side is "stuck" at k=2949008, n=150000. Please have a look at http://mersenneforum.org/showthread.php?t=9738 for information. Any help is welcome!

[siegert81]

Cool. Well, I'm glad it's being worked on. I'm also glad to see that the S/R numbers for base 3 are only in the billions, as opposed to a 20 digit number!

I may have to return when I buy a new computer...

[PawnProver44]

Originally Posted by Citrix

Just curious, why base 5 and not 3 or 7?

Also, could you provide the weights for the remaining k's?

Use : -b5
for
http://pages.prodigy.net/chris_nash/psieve.html



Citrix

Yeah, I agree. We should start a base 3 project and base 7.

[VBCurtis]

Did you look at the link from post 16 (2 posts above yours)?

There's an entire subforum for these projects. Riesel base 3 is nearly tested to 25k, thanks mostly to KEP. See Conjectures R Us.

If you'd just like to find some primes, fire up BOINC and have a go at riesel base 3, or perhaps run a range of 1G from exponent 25,000 to 100,000. Once ranges are tested to 3^100000, I personally sieve from 3^100k to 3^500k and BOINC does the primality testing.

We're not far enough along yet for available testing in the top-5000 range, but that should be ready by fall.

Edit: The crus website linked from the forum lobby is down at present; the host/admin for the project has internet troubles this week. It might be a couple days till you can see the detailed status page for riesel base 3 (R3) or R7 or S3 or S7. R3 has the most work done of the bunch.