Conjectures 'R Us; searches needed

[gd_barnes]

Searches needed for Conjectures 'R Us
(n-limit search so far):

NOTE: The searches needed in this post were last updated on 1/5/2008 and is now out of date. See the web pages for searches needed.


-Sierpinski-

Base 4:
(Sieve file available to n=1M)
64494*4^n+1 (885.4K)

Base 9:
2036*9^n+1 (100K) (reserved)

Base 10:
7666*10^n+1 (195K)

Base 11:
958*11^n+1 (100K)

Base 12:
404*12^n+1 (88.5K) (reserved)

Base 16:
47 k's remaining; 38 being done by team drive #1, several unreserved
(Sieved files available for unreserved k's to n=100K)

Base 17 (all 76.5K):
(Sieve file available to n=100K)
160*17^n+1
244*17^n+1
262*17^n+1

Base 18:
122*18^n+1 (130K) (reserved)

Base 22:
1908*22^n+1 (100K)

Base 23 (all 60K; all reserved)
8*23^n+1
68*23^n+1

Base 26 (all 54K; all reserved):
32*26^n+1
65*26^n+1
155*26^n+1

Base 27 (all 25K):
342*27^n+1
398*27^n+1

Base 28 (all 5K):
k-values:
871, 1291, 1797, 2203, 2377, 3394, 4233, 4552

Base 30 (all 25K):
278*30^n+1
588*30^n+1

Base 128:
40*128^n+1 (642.8K)

Base 256:
535*256^n+1 (53.7K)
831*256^n+1 (12.5K)

New bases that can be started:
6, 19, 25, and 31


-Riesel-

Base 4 (all 100K; all reserved):
9519*4^n-1
13854*4^n-1
14361*4^n-1
16734*4^n-1
19401*4^n-1
20049*4^n-1

Base 6 (most 25K; all reserved)
k-values:
1597, 9577, 17459, 21799, 29847, 33627, 35965, 36772, 37295, 40657, 43994, 48950, 51017, 57023, 58757, 29095, 77743, 78959, 79815

Base 10 (all 195K):
4421*10^n-1
7019*10^n-1
8579*10^n-1

Base 13:
(Sieve file available to n=100K)
288*13^n-1 (66K)

Base 16 (most 25K):
33 k's available; most unreserved; see web pages

Base 22 (all 100K):
3104*22^n-1
3656*22^n-1

Base 23 (all 60K; all reserved):
194*23^n-1
404*23^n-1

Base 26:
115*26^n-1 (55K) (reserved)

Base 27 (all 25K; all reserved):
258*27^n-1
706*27^n-1

Base 28 (5K, 15K, or 25K; most unreserved):
k-values:
233, 1422, 2319, 4001, 4322, 4436, 4871, 5076, 5133, 5306, 5886, 6207, 7367, 8991

Base 30 (all 25K):
k-values:
25, 225, 239, 249, 659, 774, 1024, 1580, 1642, 1873, 1936, 2293, 2538, 2916, 3253, 3256, 3719, 4372, 4897

New bases that can be started:
19, 24, 25, and 256


-- IMPORTANT NOTE REGARDING STARTING NEW BASES --
Starting new bases can be tricky and error-prone. I only suggest starting on bases that have a specific conjectured value, otherwise there is no way to know how many k's need to be searched. If there's a "?" by it, I would suggest avoiding it. Get with me first before starting any new base. Most of the bases remaining have a high conjecture and will require a very intense initial effort.

Large projects are doing searches on bases 2, 5, and 4 Sierp. We may do some coordination on base 4 Sierp with this effort.

Bases 32 and 128 Sierp cannot be proven with current technology. See the web page for an explanation.

Everyone have fun and knock out a few k's and prove a few conjectures!


Gary

[em99010pepe]

Now you just need to explain step-by-step on how to use the softwares, where they are located to download, etc....

[jasong]

I can help with the tutorial. (this is my bookmark so that there isn't duplicate work. I'm working on it right now)

Edit: I just realized that we can use the Base-5 tutorial with a few caveats. First, the base is going to be different, hopefully people will understand the project well enough to know what to enter there. Also, after Newpgen has sieved past 2^31(a little under 2.148G) it is extremely wise to stop the sieve and continue processing with sr1sieve. To halt the sieve gracefully, which is VERY important if you want to make sure it remembers that it's past 2^31, click on the Stop button in Windows, or make the window active in Linux and press Ctrl-C. sr1sieve can be found with a Google search. Or you can simply click here. :) Type sr1sieve -h to get the instructions for sr1sieve after you get it. I'm pretty sure it's totally text-based.

[gd_barnes]

Originally Posted by em99010pepe

Now you just need to explain step-by-step on how to use the softwares, where they are located to download, etc....

That is in the works. A lot of info. to post.

A quick answer for experienced base 2 searching folks: Use srsieve/sr1sieve/sr2sieve for sieveing and LLR for searching just like you would for base 2. But after LLR finds a "probable prime", use PFGW to prove it prime. Note that LLR will convert bases 4, 8, 16, 32, etc. to base 2 and will prove them so no need for the PFGW step if you're searching those bases.

Alternatively you could use PFGW solely for searching but LLR is still faster even with the added PFGW step to prove the primes. For those who have PFGW but haven't used it much, here are the commands to force a deterministic proof (not a probable prime):

Sierpinski primes:
pfgw -q12345*6^7890+1 -t -f0

Riesel primes:
pfgw -q12345*6^7890-1 -tp -f0

If that doesn't work, put the equation part in quotes, i.e. -q"12345*6^7890-1". My version of PFGW doesn't take quotes but it seems that some do.

After posting a reservation thread next, I'll put some software links and instructions out there for those who have done little prime searching.


Gary

[gd_barnes]

Originally Posted by jasong

I can help with the tutorial. (this is my bookmark so that there isn't duplicate work. I'm working on it right now)

Great, Jasong; thanks! Will you have links to applicable software with instructions on how to use?


Gary

[jasong]

Originally Posted by gd_barnes

That is in the works. A lot of info. to post.

A quick answer for experienced base 2 searching folks: Use srsieve/sr1sieve/sr2sieve for sieveing and LLR for searching just like you would for base 2. But after LLR finds a "probable prime", use PFGW to prove it prime. Note that LLR will convert bases 4, 8, 16, 32, etc. to base 2 and will prove them so no need for the PFGW step if you're searching those bases.

Last time I tried to use pfgw, it didn't work properly, if you're a Linux user, do some research before trusting pfgw. If you're using Linux and you are unable to verify that pfgw is reliable for Linux(they may have fixed it since then), then a Windows box is necessary for the pfgw step.

[gd_barnes]

Originally Posted by jasong

Last time I tried to use pfgw, it didn't work properly, if you're a Linux user, do some research before trusting pfgw. If you're using Linux and you are unable to verify that pfgw is reliable for Linux(they may have fixed it since then), then a Windows box is necessary for the pfgw step.

If PFGW does not work for Linux users, does Proth work? Proth can prove any base for -1 or +1. It is just much slower. It's actually what I used until Rogue informed me a week or so ago about the deterministic proof in PFGW.

Alternatively if people cannot prove them, I'll be glad to do the proving for them. They just need to let me know that they found a probable prime. Determining primality on a large group of moderate-sized probable primes is fast for PFGW. It's when testing large #'s of composite ones in the first place that LLR is faster.


Gary

[gd_barnes]

Originally Posted by jasong

Edit: I just realized that we can use the Base-5 tutorial with a few caveats. First, the base is going to be different, hopefully people will understand the project well enough to know what to enter there. Also, after Newpgen has sieved past 2^31(a little under 2.148G) it is extremely wise to stop the sieve and continue processing with sr1sieve. To halt the sieve gracefully, which is VERY important if you want to make sure it remembers that it's past 2^31, click on the Stop button in Windows, or make the window active in Linux and press Ctrl-C. sr1sieve can be found with a Google search. Or you can simply click here. :) Type sr1sieve -h to get the instructions for sr1sieve after you get it. I'm pretty sure it's totally text-based.

This is a very good start. I'll post some more formalized step-by-step instructions on the entire sieve and search process that I think works best for multiple bases sometime later tonight. My hope is to make it turnkey so that a brand new prime searcher can get started with it. I can't speak for Linux users though. If you don't mind, I'll refer them to you if needed. Thanks for your help.

The reservations/statuses thread is now up and ready to go. Grab a few k if you're so inclined! The last time I counted, there were 65 of them and I'll be adding 60+ on Sunday. I'll also start working on brand new base 24 at that point and search it to a low level like n=5K. That should yield an additional 50-100 k's for people to search.


Gary

[gd_barnes]

I have completed Base 16 Sierpinski to n=25K. 57 k's are remaining that need primes. I removed all k's with higher primes found by other projects but if you found one that I missed, let me know.

You can view the k's by going through the main Sierp page or through the main reservations page. Both have links to a new page that I created for base 16 Sierp reservations. But for ease of reference, here is a direct link: Base 16 Sierp reservations.

Come and get 'em while they're hot! Base 16 LLR's as fast as base 2 for primes of similar size, i.e. k*16^n+1 is as fast as k*2^(4n)+1.

If you have a minute, you might check some of the new links on the original pages that are pointing to the base 16 reservations page as well as the ones on the new page that point to other pages. Let me know if you find any problems.


Gary

[robert44444uk]

Originally Posted by gd_barnes

I have completed Base 16 Sierpinski to n=25K. 57 k's are remaining that need primes. I removed all k's with higher primes found by other projects but if you found one that I missed, let me know.

You can view the k's by going through the main Sierp page or through the main reservations page. Both have links to a new page that I created for base 16 Sierp reservations. But for ease of reference, here is a direct link: Base 16 Sierp reservations.

Come and get 'em while they're hot! Base 16 LLR's as fast as base 2 for primes of similar size, i.e. k*16^n+1 is as fast as k*2^(4n)+1.

If you have a minute, you might check some of the new links on the original pages that are pointing to the base 16 reservations page as well as the ones on the new page that point to other pages. Let me know if you find any problems.


Gary

I hadn't realised that the partial factorisation for k=2500 also gave a trivial result for odd k. Thats interesting.

[gd_barnes]

Originally Posted by robert44444uk

I hadn't realised that the partial factorisation for k=2500 also gave a trivial result for odd k. Thats interesting.

Well...for once, it's nice to know that I found something NEW instead of something OLD. I have found this to be a very interesting excursion into the world of factoring. It's never failed to surprise me what I come up with on some of this stuff to avoid having people search barren k's. Isn't that very strange that k=2500 is the only KNOWN k (that I am aware of) for Sierp Base 16 that has algebraic factors below the conjectured Sierp k? (Math disclaimer: Don't take me 100% literally on that statement. I suppose others 'might' have algebraic factors but if they do, they most likely have a very low prime at n=1 or 2. I haven't checked for that possibility.)

I attempted to generalize it like I did for Riesel bases 12 and 29 because that is how one learns how often and it what manner these kind of factors 'repeat' so to speak. If I had a second such situation that occured, I think I could. But alas, I couldn't come up with anything and it would take too long to extend the k's searched until a second such equation was found.

Riesel base 12 was the most misleading one to generalize. I had initially assumed that the algebraic factors for 27*12^n-1 would occur for all k=m^3. Testing proved otherwise. They only occur for every k=3*m^2! While that one was the most misleading, Riesel base 28 had the most unusual 'repeating' sequence. Algebraic factors there occur only when k=m^2 AND k==(12 or 17) mod 29.

Just when you think you have these things figured out, something new comes along! One thing I've concluded: If there's a larger percentage than usual of k=m^2 or k=m^3 remaining, you have to check them for algebraic factors. That should be a no-brainer but you never know. Some of them simply cannot be factored and are frequently just very low weight.


Gary