other conjectures

[rogue]

Originally Posted by KEP

In most cases it most likely will. However, there is for the SG conjecture, only 32 k's remaining. So we would sieve a lot of unnecessary k's and we would have to repeat the testing 100,000,000 times to cover all n. I have no means to test if handeling 100M n files and combining the candidates remaining into 1 sievefile, from wich unneeded k's is removed, is actually faster than sieving all 32 k's using srsieve (tried srsieve2, but it crashed when switching to generic sieve).

Send me the file that crashes srsieve2.

I'm trying to understand your goal. Are you trying to find the smallest n that yields an SG prime for each k? I was thinking of the search over at PrimeGrid where they are searching for SG primes with a specific bit length (or small range of them).

gfndsieve is the best sieve for b=2 and c=+1 as it sieves for a range of n and k. One could let it sieve to some prime to eliminate SG candidates because k*2*n+1 has a factor. One could then manipulate the output file with a script to convert k and n (for 2*(k*2^n+1)-1) then re-run gfndsieve starting at p=3. When done, convert k and n back.

[KEP]

Originally Posted by rogue

Send me the file that crashes srsieve2.

I'm trying to understand your goal. Are you trying to find the smallest n that yields an SG prime for each k? I was thinking of the search over at PrimeGrid where they are searching for SG primes with a specific bit length (or small range of them).

gfndsieve is the best sieve for b=2 and c=+1 as it sieves for a range of n and k. One could let it sieve to some prime to eliminate SG candidates because k*2*n+1 has a factor. One could then manipulate the output file with a script to convert k and n (for 2*(k*2^n+1)-1) then re-run gfndsieve starting at p=3. When done, convert k and n back.

It crashed srsieve2 version (older version - something with .20) - when the input was a file containing the sequences remaining in a file with same structure as srbase pl_Remain.txt file. It didn't help to try and sieve from around p=102M to p=10G - it still crashed.

Yes, I'm trying to find a SG prime for each k not yet having one. Since there is 32 k's remaining, they just like srbase does, have to be fixed, while the n range covers a lot of n.

It seems sound, what you suggest, but it still doesn't remove the n's that are looners and maintain in the output file or am I missing something (most likely)?

[rogue]

Originally Posted by KEP

It crashed srsieve2 version (older version - something with .20) - when the input was a file containing the sequences remaining in a file with same structure as srbase pl_Remain.txt file. It didn't help to try and sieve from around p=102M to p=10G - it still crashed.

Yes, I'm trying to find a SG prime for each k not yet having one. Since there is 32 k's remaining, they just like srbase does, have to be fixed, while the n range covers a lot of n.

It seems sound, what you suggest, but it still doesn't remove the n's that are looners and maintain in the output file or am I missing something (most likely)?

For a large range of n, it probably isn't as practical for gfndsieve. That program excels with a large range of k.

I just need the input files that are causing it to crash. Please post them here or send a link via e-mail or PM so that I can determine if the current version has the issue.

[JeppeSN]

What are the size of the 32 k values? What k do you consider; the odd multiples of 3?

PrimeGrid has used TwinGen (it seems) to sieve for a fixed n. Their aim has been to find the largest Sophie Germain primes (and they have succeeded).

EDIT: Sorry, I see the complete explanation in the page linked from the first post above, so forget my questions.

/JeppeSN

[rogue]

You can find twingen/twingenx here: http://www.underbakke.com/primes/

[KEP]

Originally Posted by rogue

For a large range of n, it probably isn't as practical for gfndsieve. That program excels with a large range of k.

I just need the input files that are causing it to crash. Please post them here or send a link via e-mail or PM so that I can determine if the current version has the issue.

I have no other files, than the sequence list, but I tried rerunning - again - and now have some data for you:

Sequence file is: K-list.txt (contains 32 k's remaining for SG conjecture - should be attached)

srsieve2 is version 1.1 and is started using following entry in commandprompt:

srsieve2 -P 10e9 -W 4 -w 10000000 -s"K-list.txt" -n 1 -N 100e6

It starts well, but at unknown point it starts taking up almost 4 GB of RAM, short before the final mod error message... the data from commandprompt is here:

Sieving with generic logic
Sieve started: 2 < p < 1e10 with 3200000000 terms (1 < n < 100000000, k*2^n+c) (expecting 3103670401 factors)
p=109, 0.262 p/sec, 2298312447 factors found at 3.571M f/sec, 0.0% done.
39*2^3-1 is prime!
p=389, 0.787 p/sec, 2477042934 factors found at 3.464M f/sec, 0.0% done. ETC 2619-11-27 03:30
279*2^1-1 is prime!
351*2^1-1 is prime!
387*2^1-1 is prime!
399*2^1-1 is prime!
Sieving with generic logic
Split 32 base 2 sequences into 4149 base 2^360 sequences.
Fatal Error: 387*2^25206-1 mod 809 = 297ctors found at 3.101M f/sec, 0.0% done.

The exact same happens, if I use a deeper sieved .abcd file. It starts and then stacks a lot of RAM before exiting with a mod error :(

It should not be on your top priority list to make a new siever, since I have gotten something working in regard of testing the n<=100M range for the 32 k's for SG, using sr2sieve, but for the future users it sure would save them some troubles if there were a dedicated siever made for variable n and various amounts of fixed k's sieving for SG.

[sweety439]

Originally Posted by sweety439

This page is only for the twin case and the Riesel case, for the Sierpinski case, see http://harvey563.tripod.com/cunninghams.txt

An interesting one is k=279, there is no known twin prime (k*2^n-1 and k*2^n+1), neither known 1st kind Sophie-Germain prime/Cunningham chain (k*2^n-1 and k*2^(n+1)-1) or known 2nd kind Sophie-Germain prime/Cunningham chain (k*2^n+1 and k*2^(n+1)+1)

Twin prime: CK=237
1st kind Sophie-Germain prime/Cunningham chain: CK=807
2nd kind Sophie-Germain prime/Cunningham chain: CK=32469

There is no known twin prime for some even k divisible by 3, e.g. k=312 (since all n must be >=1)

[sweety439]

Originally Posted by gd_barnes

I'm with Sweety on this one. (Surprise, surprise! ) You did not read his request carefully. Please reread it and consider a more nuanced response. His complaint is one that I had about srsieve when I was working on the same conjectures that he was about a year ago. They are some conjectures that are fairly interesting and have been previously worked on by several others long before him and me.

There is no reason for srsieve to immediately error out candidates that are divisible by 2 since it should automatically remove them anyway in the normal course of sieving. By automatically errorring them out such tests that he is referring to cannot be properly sieved.

It would be like having srsieve automatically erroring out candidates that are divisible by 3 before doing actual sieving on them. It is an uneccesary error check that prevents other kinds of sieving from being done.

Well, you said these conjectures would have to have multiple and separate sieves done (see your post https://mersenneforum.org/showpost.p...&postcount=243), however, you can we use srsieve to sieve the sequence k*b^n+-1 for primes p not dividing gcd(k+-1,b-1), and initialized the list
of candidates to not include n for which there is some prime p dividing gcd(k+-1,b-1) for which p dividing (k*b^n+-1)/gcd(k+-1,b-1) (like we can initialized the list
of candidates to not include n for which k*b^n+-1 has algebra factors, e.g. for square k's for k*b^n-1, we can remove all even n in the sieve file, and for cube k's for k*b^n-1 and k*b^n+1, we can remove all n divisible by 3 in the sieve file)

However, I only did the first step (sieve the sequence k*b^n+-1 for primes p not dividing gcd(k+-1,b-1)), like my sieve files for R36, SR46, and SR58, e.g. for R36 ((k*36^n-1)/gcd(k-1,36-1)) I sieved start with the prime 11, since we should not sieve the primes 5 and 7, I do not know how to remove the n's with a given property, I want to know how you remove the n for which k*b^n+-1 has algebra factors, e.g. remove all n divided by 4 from the sieve file of S230 k=4, I can also use this way to remove n for which there is some prime p dividing gcd(k+-1,b-1) for which p dividing (k*b^n+-1)/gcd(k+-1,b-1)

[kar_bon]

There're two problems with the example of 13*43^n-1:

1. All candidates are divisible by 6.
2. The smallest p-value to start with srsieve is p=44, so have to be greater than the base.

What I did:
- looking the factorizations of the first values of (13*43^n-1)/6
- every n==0 mod 2 has factor 2
- every n==1 mod 3 has factor 3
- every n==3 mod 4 has factor 5
- every n==6 mod 8 has factor 17
- every n==1 mod 30 has factor 31
- every n==6 mod 22 has factor 23

Using awk with this:

BEGIN {print "44:M:1:43:258" >"t.txt"
  n=1
  while (n < 1000000)
  {  if (n % 2 == 0) {}		# factor 2
     else if (n % 3 == 1) {}	# factor 3
     else if (n % 4 == 3) {}	# factor 5
     else if (n % 8 == 6) {}	# factor 17
     else if (n % 30 == 1) {}	# factor 31
     else if (n % 22 == 6) {}	# factor 23
     else 
       print "13 "n >>"t.txt"
     n++    
  }
}

creates "t.txt" like (in seconds)

44:M:1:43:258
13 5
13 9
13 17
13 21
13 29
13 33
13 41
13 45
13 53
13 57
(...)

for n<1M.
Use sr1sieve on this to higher P.

Changing the header after sieve to

ABC ($a*43^$b-1)/6
13 41
13 101
13 149
13 165
13 173
13 185
13 233
(..)

and test it with PFGW.
I got ~26,000 candiates left (don't know the exact P-value, was only a quick test).

[gd_barnes]

OK so (13*43^n-1)/2 is a bad example.


A better example is (13*51^n-1)/2


Regardless we want srsieve to do this. Removing the error check from srsieve is the easiest way for the layman.

[sweety439]

Originally Posted by gd_barnes

Please change srsieve to remove the error check for divisibility by 2 and then force the regular sieve process to remove the terms divisible by 2 instead. Is that really difficult? It seems like a simple fix. I'm pretty sure I or others have requested this before and we seem to keep getting the run-around about it.

To be more specific below is what Sweety and I and others want to do when attempting to test a conjecture such as (13*43^n-1)/2 if the form is not found to have a smallish prime using simple trial factoring with PFGW.

1. Sieve using srsieve using the form 13*43^n-1 but with a starting sieve depth of 3 using the following command:

srsieve -G -p 3 -P 1e9 -n 25e3 -N 100e3 -m 1e9 "13*43^n-1"

This tells srsieve to only sieve the form for P=3 to 1e9. That way it does not remove the terms that are divisible by 2 (which would be all of them in this case).

2. Test with PFGW using a standard PFGW header of:
(ABC $a*43^$b-1)/2 // {number_primes,$a,1}
13 25007
13 25019
(etc.)

This allows us to both sieve and test the form (13*43^n-1)/2. Srsieve currently works for us if we have a form with a prime divisor other than 2 such as (13*46^n-1)/3. In that case we would just have it sieve the range of P=5 to 1e9 and there would be no error as there is in the case of (13*43^n-1)/2.

Does this make sense?

[ All of these are examples. They are not actual work done.]

If this cannot be done please let us know and we will not request it anymore. We would prefer not to have to run a separate program when standard srsieve will work for 99% of cases like this. Also please let us know how you would sieve the form (13*43^n-1)/2. That would be very helpful.

The divisor of k*b^n+-1 (+ for Sierp, - for Riesel) is always gcd(k+-1,b-1) (+ for Sierp, - for Riesel) (see post https://mersenneforum.org/showpost.p...&postcount=230), since gcd(k+-1,b-1) is the trivial factor of k*b^n+-1, it is simply to take out this factor, thus, the divisor of R43, k=13 is 6, not 2 (gcd(13-1,43-1) = 6), and the formula of R43, k=13 is (13*43^n-1)/6, not (13*43^n-1)/2