Conjectures 'R Us; searches needed

[gd_barnes]

Originally Posted by japelprime

I think I will try Base 9: 2036*9^n+1 (100K - 200k)

Is that ok or have someone alredy started working on this number?

I have alredy sieved the file to 5,5G with NewPgen and have now started seiving with SR2Sieve.

Thanks and welcome to the effort Japelprime!

That one is not taken. I'll reserve it for you. That's a good choice too because it would be a GREAT one to find a prime for. Not only would it make the top-5000 list if the prime is n>105200, it would prove the conjecture!

FYI, you might consider using sr1sieve instead of sr2sieve for just one equation like this. It will be over twice as fast and you don't have to mess with removing factors at the end. Sr2sieve is better for sieving 2-3 or more equations. If there are any questions about that or anything else, please let us know. I or several others can answer.


Gary

[japelprime]

Thanks Gary.

sr2sieve is doing fine with 741kp/sec but I will see if sr1sieve is doing better.
I was not aware of that sr1sieve remove the factors.

[mdettweiler]

Originally Posted by japelprime

Thanks Gary.

sr2sieve is doing fine with 741kp/sec but I will see if sr1sieve is doing better.
I was not aware of that sr1sieve remove the factors.

It will remove the factors as long as you use the -o command line switch to specify an output file.

[japelprime]

Originally Posted by Anonymous

It will remove the factors as long as you use the -o command line switch to specify an output file.

Thanks Anonymous.

[Citrix]

Here is a covering set for base 31 sierpinksi. You can try constructing the lowest such number using this set.
(13,37,7,19,331,922561,577,3637,81343,1536553,1538083,512616735577)

[robert44444uk]

Base 31, Sierpinski why not just 7; 13; 19; 37; 331 with 12-cover? The solution is less than 10^7

[gd_barnes]

Originally Posted by robert44444uk

Base 31, Sierpinski why not just 7; 13; 19; 37; 331 with 12-cover? The solution is less than 10^7

You beat me to the punch Robert. I was testing this up until k=10M like I had mentioned previously when you posted this. I also was expecting the same or a similar covering set as the Riesel conjecture.

The Sierpinski conjecture for base 31 is k=6360528. The covering set is as you said.


Gary

[gd_barnes]

I have renamed this thread to 'searches needed' instead of 'primes needed' to avoid confusion with the new 'report primes here' thread.

[gd_barnes]

I updated the searches needed for several bases and added 2 k's that need to be searched for Sierp base 256.

535*256^n+1 has already been searched to top-5000 territory (n=53.7K) so that's one that someone may want to reserve. The search limit was converted from the search limit of n=430K for 535*2^n+1 on the Prothsearch pages.


Gary

[geoff]

How are people searching for covering sets to conjecture Sierpinski/Riesel numbers? If someone can suggest an algorithm I would be happy to try to implement it in C/ASM.

[gd_barnes]

Originally Posted by geoff

How are people searching for covering sets to conjecture Sierpinski/Riesel numbers? If someone can suggest an algorithm I would be happy to try to implement it in C/ASM.

That would be great and it's interesting that you asked. I just run all possible k's that don't have trivial factors through srsieve for the range of n=1-10K up to P=25K; about 100000 k's at a time. Whatever the first k is that it removes from the sieve is the conjecture. I then just go to Alperton's site and figure out the covering set. This is dead-on accurate assuming that a covering set doesn't include a factor > 25K (highly unlikely I think).

It was pretty ugly but highly effective and accurate and I came up with lower conjectures that way in 3-4 cases than were previously shown in the various threads for bases 6-18, 10, 22, 23, etc. There is one exception to the 'highly effective' statement. Since srsieve only allows slightly > 100000 k's at a time, it takes quite a while to go much beyond k=2-3M, which requires all manual effort. Sierp base 31 (conjecture k>6M) took 1-2 hours of manual effort on my part to come up with and of course it's impossible for bases 3, 7, and 15, although I was able to determine that the conjectures for base 3 and base 7 had to be k>2M and k>200K respectively.

Robert and Citrix seem to know the math behind searching various covering sets and how to come up with one in the first place. I'd be curious to see it myself.


Gary