Starting new bases

[MrOzzy]

Admin edit: For starting new bases, it is recommended that the below PFGW scripts for new bases be used as input to PFGW. There are 2 different versions. One for PFGW 3.2.3 and earlier and one for PFGW 3.2.7 and later. Running the later version is highly recommended. For the latest PFGW version, see the "PFGW latest well tested version" thread.

PFGW 3.2.3 and earlier: new-bases-4.1
PFGW 3.2.7 and later: new-bases-4.3

I've been searching these forums for several days now, and as a result my head hurts and it is yelling "too much information". I just need to find the answer to some simple questions:

Say for example I want to start some random base in Sierpinski or Riesel.

How do you:

1. Find out whether this base already has been tested and how far, who reserved it ect, ...
2. If nobody is working on it or has been working on it how do you find the conjecture with its covering set?
3. How do you start sieving files, which programs do you use ect ...
4. What should you use to test the remaining n? (or k). I did some small tests with newpgen to run the sieve and llr to test the remaining n and all I got was "ERROR!!" as a result of my effort :)

[Flatlander]

Originally Posted by MrOzzy

Say for example I want to start a some random base in Sierpinski or Riesel.

How do you:

1. Find out wether this base already has been tested and how far, who reserved it ect, ...
2. If nobody is working on it or has been working on it how do you find the conjecture with its covering set?
3. How do you start sieving files, which programs do you use ect ...
4. What should you use to test the remaining n? (or k).)

I would like to know this too.

[Siemelink]

Originally Posted by MrOzzy

I've been searching these forums for sevral days now, and as a result my head hurts and it is yelling "too much information". I just need to find the answer to some simple questions:

Say for example I want to start a some random base in Sierpinski or Riesel.

How do you:

1. Find out wether this base already has been tested and how far, who reserved it ect, ...
2. If nobody is working on it or has been working on it how do you find the conjecture with its covering set?
3. How do you start sieving files, which programs do you use ect ...
4. What should you use to test the remaining n? (or k). I did some small tests with newpgen to run the sieve and llr to test the remaining n and all I got was "ERROR!!" as a result of my effort :)

1) Check out http://noprimeleftbehind.net/crus/Ri...onjectures.htm
2a) Run a black box program that calculates it for you. In the Crus forum there is the program by R. Gerbicz. Or you can ask me for a copy of mine.
2b) Or sieve a range of your base in srsieve and then the one that is discarded may be a Riesel or Sierpinski
2c) Or figure out how to find them yourself (not easy)
3a) First do a run with PFGW to dispose of all the small primes (see attached script)
3b) Then sieve the remaining k with srsieve
4) when you have sieved deep enough, switch to LLR or phrot.

Enjoy, Willem.

[MrOzzy]

Originally Posted by Siemelink

1) Check out http://gbarnes017.googlepages.com/Ri...onjectures.htm
2a) Run a black box program that calculates it for you. In the Crus forum there is the program by R. Gerbicz. Or you can ask me for a copy of mine.
2b) Or sieve a range of your base in srsieve and then the one that is discarded may be a Riesel or Sierpinski
2c) Or figure out how to find them yourself (not easy)
3a) First do a run with PFGW to dispose of all the small primes (see attached script)
3b) Then sieve the remaining k with srsieve
4) when you have sieved deep enough, switch to LLR or phrot.

Enjoy, Willem.

Thanks for your answers. I have a few more questions though:

2a) This program by R. Gerbicz (covering.exe) requires an exponent. What is the meaning of this exponent?
3a) How is PFGW related to that attached script?
3b) How do you know if you have sieved deep enough
4) How should you determine if you should use LLR or phort?

One of the reasons I ask this questions is to lower the step for people interested. Sooner or later a sticky topic with the needed info could be handy and interesting for potential sievers or prime hunters.

[Siemelink]

Originally Posted by MrOzzy

Thanks for your answers. I have a few more questions though:

2a) This program by R. Gerbicz (covering.exe) requires an exponent. What is the meaning of this exponent?
3a) How is PFGW related to that attached script?
3b) How do you know if you have sieved deep enough
4) How should you determine if you should use LLR or phort?

One of the reasons I ask this questions is to lower the step for people interested. Sooner or later a sticky topic with the needed info could be handy and interesting for potential sievers or prime hunters.

2a) I forgot. Experiment with the program so that you can find known values.
3a) pfgw.exe scr.txt -f100 on the command line
3a) winpfgw.exe and then enter scr.txt -f100 in windows
3b) when the removal rate per minute is lower then what you get with LLR
4) Use LLR.

Willem.

[gd_barnes]

I'm sorry I haven't had much time lately. These are great questions and Willem referred you to both the correct link with instructions and did a good job of answering them.

Starting new bases is EXTREMELY tricky and in the instructions that I prepared that he provided the link to, I suggested that you contact me when starting a new base. But Willem is now a resident expert in starting them and I'm glad he stepped in.

I realize that starting new bases is fun and interesting but my preference is that people search for bases <= 32 or bases that are powers of 2 up to 256.

If you can tell Willem or me what base you are interested in starting, we could give you the particular details and pitfalls of that particular base. Suggestion: When starting out, find a base with a relatively low conjecture.

As for the exponent, I suggest using either 24 or 144 most of the time. The exponent refers to how many n-values it takes before the covering set of factors repeats. For instance, if a k for a base has the following factors for the following modulos of n:

n : factor
(0 mod 4) : 5
(1 mod 4) : 3
(2 mod 4) : 7
(3 mod 4) : 3

It would be said to have a 'period' (or in the case of the "covering" program...'exponent'), of 4 because the factors repeat every 4 n-values.

Don't concern yourself if you don't get the math here, I'd just suggest using an exponent of 24 or 144.


Gary

[MrOzzy]

Thanks for all the info.

I've been playing around with everything a little bit and I have a few more questions:

- This pgfw script seem to be made for Sierpinski only, is there a Riesel one available too?
- covering.exe you a conjectured K and the primes considered to calculate the conjectured K, but it doesn't tell which primes are used when a solution is found. How do I calculate which primes are used for the covering set?

[Siemelink]

Originally Posted by MrOzzy

Thanks for all the info.
- This pgfw script seem to be made for Sierpinski only, is there a Riesel one available too?

Change a plus into a minus where apropriate.

[gd_barnes]

Originally Posted by MrOzzy

Thanks for all the info.

I've been playing around with everything a little bit and I have a few more questions:

- covering.exe you a conjectured K and the primes considered to calculate the conjectured K, but it doesn't tell which primes are used when a solution is found. How do I calculate which primes are used for the covering set?

I think covering.exe gives a set of them that it used but those are almost always way more factors than what is needed and is not what we're looking for. What I generally do is do it manually by going to:
http://www.alpertron.com.ar/ECM.HTM. It is a great program that will prime factor large numbers up to 10000 digits.

I plug in the form and try n=1, 2, 3, etc. I then analyze the least set of factors that makes them all composite. You have to be careful because it's easy to get a factor in there that you don't need. To be mathematically correct, we want the smallest covering set that makes the conjectured k always composite.

To get a good feel for it, play around with a known small conjecture such as Riesel base 8 with a (now proven) conjecture of k=14 and a covering set of [3, 5, 13]. See how the pattern of factors repeats for 14*8^n-1 with the different n-values. Once you do that, you should be able to do it with any base.

Covering.exe is pretty good at coming up with the lowest conjecture if it is given reasonable parameters. It's not so good at coming up with the smallest covering set.


Gary

[MrOzzy]

I was playing around a little bit with everything and I got this when I ran srsieve using the output from pgfw: "removed candidate sequence 30*117^n-1 from the sieve"
.. but it doesn't say why ...

[ValerieVonck]

Hi! can anyone please explain what covering does???

I plugin following numbers:

104
2
-1
500000
3 5 13
Checking k*2^n-1 sequence for exponent=104, bound for primes in the covering set
=500000, bound for k is 3
Examining primes in the covering set: 3,5,17,8191,2731,53,157,1613
And their orders: 2,4,8,13,26,52,52,52

Base = 104
2 = exponent
-1 = Riesel
500000 = k ??
??

Thank you!