Generalized Cullen and Woodall Searches
 

If you are interesting in searching for primes of the form n*b^n-1, aka Generalized Woodalls, check out [URL="http://harvey563.tripod.com"]Steven Harvey's website[/URL]. In covers bases up to b=10000. The Prime Pages has a [URL="http://primes.utm.edu/top20/page.php?id=45"]Top 20[/URL] list for Generalized Woodalls.

If you are interesting in searching for primes of the form n*b^n+1, aka Generalized Cullens, check out [URL="http://www.loeh.name/guenter/gc/status.html"]Guenter Loeh's website[/URL]. In only covers bases up to 100. Daniel Hermle had a website that covered from b=101 to b=200, but that site is no longer available. I've asked Steven Harvey to see if he is interested in taking over coordination of the Generalized Cullen search for b > 100. The Prime Pages has a [URL="http://primes.utm.edu/top20/page.php?id=42"]Top 20[/URL] list for Generalized Cullens.

To participate in these searches you need to use [URL="https://sites.google.com/site/geoffreywalterreynolds/programs/gcwsieve"]gcwsieve_smallp[/URL] or MultiSieve and sieve to p > n. You can then switch to [URL="https://sites.google.com/site/geoffreywalterreynolds/programs/gcwsieve"]gcwsieve[/URL]. Note that I have no desire to support or modify MultiSieve, so I suggest that you use gcwsieve_smallp.

I'm working on a mod to gcwsieve that will allow one version to do what you now need two programs to do. I could probably release that at any time.

I'm also working on an OpenCL implementation of gcwsieve. It has a number of bugs and is not optimized, so it will be a while before it is released.

Once sieving is done you can use LLR or PFGW to do the primality testing. And if you have multiple cores you can use PRPNet to manage your search.

I have Cullen sieve files for b=3 through b=200 for all n<1e6. If you are interested, please e-mail me (don't PM since I can't send attachments via PM). You'll have to remove n that have already been tested before you continue to sieve.

Gunther tells me that Daniel intends to get his website back online, but he has no date for that.

If you choose to test for 100 < b <= 200, you can post results here and we'll coordinate with Daniel when he gets his site back up.

coordination of Generalized Cullen searches
 

I will keep track of any GC search results that anyone wishes to send me at my site harvey563.tripod.com (for bases higher than 100)
You can send me reservations and reports to [email]harvey563@yahoo.com[/email] or you can message me on this forum.

StevenHarvey

:spot:

gc b201-300
 

a few weeks ago i did some work for base b201-300.
sieving and prptesting, and sieving is still in progress ...

What is the upper bound for your search?

[QUOTE=rogue;387108]What is the upper bound for your search?[/QUOTE]

first goal is to create sieve files to N=1e6, P=100e9.
second is to test all of them to n=50e3.

at present b=201-250 prptested to n=10e3 and b=251-300 to n=5e3.

i'll update my stats pages soon.

I am currently sieving all bases for 101 <= b <= 10000 up to n=10000. That should be done by the weekend. I will start PRP testing in about two weeks. When that is done I'll provided a page for Steven to post on his website.

i'm late. sorry!

my results for generalized cullen b=201-300 to n=10e3.
[url]http://primes.ctrl-x-c.de/files/gc_b201-300_n1-10e3.tar[/url]

my page: [url]http://primes.ctrl-x-c.de/files/primelist_testlimit[/url]
i can update the if necessary

[QUOTE=grueny;391206]i'm late. sorry!

my results for generalized cullen b=201-300 to n=10e3.
[url]http://primes.ctrl-x-c.de/files/gc_b201-300_n1-10e3.tar[/url]

my page: [url]http://primes.ctrl-x-c.de/files/primelist_testlimit[/url]
i can update the if necessary[/QUOTE]

That will save me a little time.

I have a small program that will take all of the primes, then generate a list in the same format that Steven uses for Generalized Woodalls. It will also merge with the known results of Daniel Hermle.

[QUOTE=grueny;391206]i'm late. sorry!

my results for generalized cullen b=201-300 to n=10e3.
[url]http://primes.ctrl-x-c.de/files/gc_b201-300_n1-10e3.tar[/url]

my page: [url]http://primes.ctrl-x-c.de/files/primelist_testlimit[/url]
i can update the if necessary[/QUOTE]

BTW, how long did it take you to PRP test that range? How deeply did you sieve? I you are interested in taking on other ranges for n <= 10000 and b <= 10000, please PM me your e-mail and I can send you some pre-sieved ranges (up to p=1e9).

With help from grueny, all bases from 101 to 10000 have been searched to to n=10000. I have attached the list for Steven to post on his website.

There are two things to note. First, for bases 101 to 200, this list is merged with what Daniel Hermle had on his website, but since the internet wayback machine does not have some of his pages archived, any primes found on his search for n > 10000 are lost and those ranges need to be redone. He has told me via e-mail that he has that information, but until I get it, I will not include those results. Second, I excluded primes for n=1. Someone is welcome to retest these 9900 bases for n=1 to fill in that gap.

[QUOTE=rogue;394233]With help from grueny, all bases from 101 to 10000 have been searched to to n=10000. I have attached the list for Steven to post on his website.

There are two things to note. First, for bases 101 to 200, this list is merged with what Daniel Hermle had on his website, but since the internet wayback machine does not have some of his pages archived, any primes found on his search for n > 10000 are lost and those ranges need to be redone. He has told me via e-mail that he has that information, but until I get it, I will not include those results. Second, I excluded primes for n=1. Someone is welcome to retest these 9900 bases for n=1 to fill in that gap.[/QUOTE]

There seems to be an error of omission on the line for base 162:

162 [ 95000] 2, 31, 135, 847, 139, 7255, 34051

That 139 should be 1339.

Hmm. I'll have to take a look and see what I did to mess that up.

[QUOTE=rogue;394233]Someone is welcome to retest these 9900 bases for n=1 to fill in that gap.[/QUOTE]

I did a few updates to your GC list:[LIST][*]For b=162 the 139 was corrected to 1339.[*]The primes for n=1 are added (1203 in total).[*]Some other missing primes found by Kosmaj and myself (e.g. for bases 216, 256, 7776, 8192 and a few more) were also added.[*]And finally I updated some of the test limits according to our notes and records. Some of this information dates back to communication with Daniel Hermle a few years ago (e.g. some of the progress in the b=101-200 interval is actually his work).[/LIST]
While working with your file I noticed a few cases where the n values are out of order, e.g. for b=3164 and b=3168.
So far I only corrected this for b=3168, which I tested up to n=4000.

[QUOTE=Thomas11;394537]I did a few updates to your GC list:[LIST][*]For b=162 the 139 was corrected to 1339.[*]The primes for n=1 are added (1203 in total).[*]Some other missing primes found by Kosmaj and myself (e.g. for bases 216, 256, 7776, 8192 and a few more) were also added.[*]And finally I updated some of the test limits according to our notes and records. Some of this information dates back to communication with Daniel Hermle a few years ago (e.g. some of the progress in the b=101-200 interval is actually his work).[/LIST]
While working with your file I noticed a few cases where the n values are out of order, e.g. for b=3164 and b=3168.
So far I only corrected this for b=3168, which I tested up to n=4000.[/QUOTE]

That is due to how I build the list. The primes were not sorted, so some might be out of sequence.

Sorry, I just noticed that I somehow messed it up and added the 1's for the GW primes instead of the GC primes.
So here comes the corrected version of the file.

I also noticed quite a few duplicates in the original file for bases < 200 and n<10. This has been corrected now, but there may be still some other cases that I missed...

I just noticed today that Steven Harvey has posted the list of Generalized Cullens for 100 < b <= 10000. All b < 201 have been searched to n=100000 and all b > 200 have been searched to 10000.

Why the page of generalized Woodall primes (n*b^n-1) has a condition that n>=b-1, but the page of generalized Cullen primes (n*b^n+1) does not have?

The pages are:

Generalized Woodall primes: [URL]http://harvey563.tripod.com/GWlist.txt[/URL]

Generalized Cullen primes: [URL]http://www.loeh.name/guenter/gc/status.html[/URL] for b<=100, [URL]http://harvey563.tripod.com/GClist.txt[/URL] for b>100.

Read this to find your answer: [url]http://primes.utm.edu/glossary/page.php?sort=WoodallNumber[/url]

[QUOTE=rogue;449315]Read this to find your answer: [URL]http://primes.utm.edu/glossary/page.php?sort=WoodallNumber[/URL][/QUOTE]

This is also true for generalized Cullen primes: [URL]http://primes.utm.edu/glossary/xpage/Cullens.html[/URL].

The difference is in the definition:

The reason for the restriction on the exponent n is simple, without some restriction every prime p would be a generalized Woodall.

so any prime that can be written in this form could be called a generalized Cullen prime

This means that some p can be generalized Cullens, but all p can be generalized Woodalls.

[QUOTE=rogue;449360]The difference is in the definition:

The reason for the restriction on the exponent n is simple, without some restriction every prime p would be a generalized Woodall.

so any prime that can be written in this form could be called a generalized Cullen prime

This means that some p can be generalized Cullens, but all p can be generalized Woodalls.[/QUOTE]

No, let n=1, then every prime p can be written as 1*(p-1)^1+1 (generalized Cullen base p-1) and 1*(p+1)^1-1 (generalized Woodall base p+1).

[QUOTE=sweety439;449365]No, let n=1, then every prime p can be written as 1*(p-1)^1+1 (generalized Cullen base p-1) and 1*(p+1)^1-1 (generalized Woodall base p+1).[/QUOTE]

ah but without base 1, 2 can't be represented that way. admittedly I didn't think of that right away either.

What is the current search limit for generalized Cullen prime base 13 (n*13^n+1)?

[QUOTE=sweety439;451320]What is the current search limit for generalized Cullen prime base 13 (n*13^n+1)?[/QUOTE]

1,000,000 per [URL="guenter.loeh.name/gc/status.html"]this[/URL].

[QUOTE=rogue;449360]The difference is in the definition:

The reason for the restriction on the exponent n is simple, without some restriction every prime p would be a generalized Woodall.

so any prime that can be written in this form could be called a generalized Cullen prime

This means that some p can be generalized Cullens, but all p can be generalized Woodalls.[/QUOTE]

However, we felt that the two sides should be consistent in their approach, in the definition of [URL="http://primes.utm.edu/glossary/xpage/Cullens.html"]http://primes.utm.edu/glossary/xpage/Cullens.html[/URL] and [URL="http://primes.utm.edu/glossary/xpage/WoodallNumber.html"]http://primes.utm.edu/glossary/xpage/WoodallNumber.html[/URL], no matter for the +1 (Cullen) side or for the -1 (Woodall) side, there is a condition that n >= b-1. However, for the sequence "numbers n such that n*b^n+-1 is prime", we can choose to allow n < b-1.

Mersennewiki page for this project: [URL="http://www.mersennewiki.org/index.php/Cullen"]http://www.mersennewiki.org/index.php/Cullen[/URL] (Cullen) and [URL="http://www.mersennewiki.org/index.php/Woodall_numbers"]http://www.mersennewiki.org/index.php/Woodall_numbers[/URL] (Woodall).

A prime is missing in [URL="http://guenter.loeh.name/gc/status.html"]http://guenter.loeh.name/gc/status.html[/URL]: 1806676*41^1806676+1, also, a prime is missing in [URL="http://harvey563.tripod.com/GClist.txt"]http://harvey563.tripod.com/GClist.txt[/URL]: 177482 *117^177482 +1

What makes you think that Loeh and Harvey read this forum?
Hint: instead, just [B]email them[/B]!

[QUOTE=Batalov;530587]What makes you think that Loeh and Harvey read this forum?
Hint: instead, just [B]email them[/B]![/QUOTE]

I know that Steven has been on this forum in the past, but is probably isn't one of his usual haunts. If you point him to this thread, then he might visit more often.

[QUOTE=Batalov;530587]What makes you think that Loeh and Harvey read this forum?
Hint: instead, just [B]email them[/B]![/QUOTE]

I emailed them, but I only have Gmail, I see Loeh's email is "guenter@loeh.name", and Harvey's email is "harvey563@yahoo.com", neither is Gmail (I use Gmail to type these two email addresses ....

Does anyone know if the lists are still actively maintained? And is the search organized in any way? PG has a generalized C/W project, but it only covers bases up to 140 or so. Where did the others originate from?



[QUOTE=sweety439;531072]I emailed them, but I only have Gmail, I see Loeh's email is "guenter@loeh.name", and Harvey's email is "harvey563@yahoo.com", neither is Gmail (I use Gmail to type these two email addresses ....[/QUOTE]What does it matter if they use gmail? Fortunately e-mail is from the golden days of internet when protocols were open standards and any e-mail provider accepts mail from any other. Imagine instant messaging to be like that.:geek:

[QUOTE=bur;562843]Does anyone know if the lists are still actively maintained? And is the search organized in any way? PG has a generalized C/W project, but it only covers bases up to 140 or so. Where did the others originate from?[/QUOTE]

You have to reach out to them to see if they are still around and actively maintaining their websites.

The searches are only coordinated from the perspective the they track reservations and completed ranges from individuals that communicate with them. They do not set up servers (BOINC or PRPNet) for outsiders to access and participate.

PrimeGrid is only searching bases (to a limit) with no known prime because those bases are interesting.

You need to remember that people set up websites for searches like this because it interests them.

If Günter and Steven are no longer interested in hosting the pages, then someone else can take ownership and coordinate continued searching for GCW primes.

Steven's last post to this forum is at the same time of his last update to his website. I have no idea what his status is. I have no biographical information on him.

Günter is 76 (per his website) with no updates in nearly a year. I have no idea what his status is either.

My [url='https://www.rieselprime.de/ziki/Statistics']Wiki[/url] got the possibility to create pages for (Near/Generalized) Cullen/Woodall search with reserving any base by a user.
For now there're only a few pages done including history taken from those pages mentioned above.
There're also pages for [url='https://www.rieselprime.de/ziki/PrimeGrid_Generalized_Cullen_Prime_Search']PG Gen.Cullen[/url] and [url='https://www.rieselprime.de/ziki/PrimeGrid_Cullen_Prime_Search']PG Cullen[/url] searches, the Woodall page is not yet created but base 2 is [url='https://www.rieselprime.de/ziki/Gen_Woodall_prime_table']reserved[/url] by [url='https://www.rieselprime.de/ziki/PrimeGrid']PG[/url], too.
Any base can be created with own page using special [url='https://www.rieselprime.de/ziki/Template_prototypes']templates[/url] for them.

Reserving 12
 

I'm reserving 12 because numbers in this sequence are considered to be Proth numbers also. (n*12^n+1)

I have contacted both Steven Harvey and Gunther Loh. They are both still managing these searches. Please reach out to them to coordinate your reservations.

Is it okay if I take back my reservation without actually doing any primality tests, or if I do the reservation, do I have to finish all of the work before releasing it?

[QUOTE=YaoPlaysMC;565588]Is it okay if I take back my reservation without actually doing any primality tests, or if I do the reservation, do I have to finish all of the work before releasing it?[/QUOTE]

This thread is not used for managing reservations. If you reserved thru Steven or Gunther, then you can unreserve thru them.

How to use LLR to primality test Gen. Cullen Primes?
 

I just want to see how long a primality test would take using LLR but I can't seem to use the files from the sieving program in LLR? Can anyone find a way to primality test Gen. Cullen primes?


Edit: I found out that you can use openPFGW to primality test these primes.

[QUOTE=YaoPlaysMC;565623]I just want to see how long a primality test would take using LLR but I can't seem to use the files from the sieving program in LLR? Can anyone find a way to primality test Gen. Cullen primes?


Edit: I found out that you can use openPFGW to primality test these primes.[/QUOTE]

You can test them with LLR, you will just need to format your candidates to a NewPGEN type header. Here is an example for n*3^n+1:

[CODE]200000:P:1:3:257
32 32
34 34
54 54
76 76
114 114
128 128
176 176
202 202
212 212
252 252
274 274
308 308
318 318
390 390
414 414
470 470
474 474
516 516
532 532
534 534
548 548
580 580
620 620
634 634
688 688
694 694
800 800
812 812
860 860
894 894
898 898
900 900
902 902
968 968
974 974
980 980
988 988[/CODE]

From srXsieve package, you can use srfile.exe to convert your sieve files to (almost) any format (like abc, abcd, pfgw, newpgen, etc), and put them in a form digested by LLR after just few trials, without much background knowledge.

[QUOTE=YaoPlaysMC;565623]I just want to see how long a primality test would take using LLR but I can't seem to use the files from the sieving program in LLR? Can anyone find a way to primality test Gen. Cullen primes?


Edit: I found out that you can use openPFGW to primality test these primes.[/QUOTE]

llr would be faster and I thought that it supported the ABC format output by gcwsieve. I'll have to take a look at llr source.

Upon review, llr supports the ABC header of "$a*$b^$a$c", but gcwsieve outputs "$a*<base>^$a$b". It shouldn't be hard to modify gcwsieve to output an llr compatible ABC format. Until I do that you have other options to modify the file so that llr can use it.

For b=12 I found a new prime (345951*12^345951+1). Almost made the top 20 generalized Cullen primes.
[C]
Special modular reduction using zero-padded AVX-512 FFT length 144K, Pass1=192, Pass2=768, clm=1 on 345951*12^345951+1
Calling Brillhart-Lehmer-Selfridge with factored part 55.79%
345951*12^345951+1 is prime! (488.4216s+0.0016s)[/C]

[QUOTE=carpetpool;565626]You can test them with LLR, you will just need to format your candidates to ...[/QUOTE]
...any appropriate format.
Format [C]ABC $a*$b^$c$d[/C] covers pretty much everything.