20140921, 22:13  #1 
"Mark"
Apr 2003
Between here and the
3×17×131 Posts 
Generalized Cullen and Woodall Searches
If you are interesting in searching for primes of the form n*b^n1, aka Generalized Woodalls, check out Steven Harvey's website. In covers bases up to b=10000. The Prime Pages has a Top 20 list for Generalized Woodalls.
If you are interesting in searching for primes of the form n*b^n+1, aka Generalized Cullens, check out Guenter Loeh's website. 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 Top 20 list for Generalized Cullens. To participate in these searches you need to use gcwsieve_smallp or MultiSieve and sieve to p > n. You can then switch to gcwsieve. 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. Last fiddled with by rogue on 20140930 at 22:07 
20140930, 22:11  #2 
"Mark"
Apr 2003
Between here and the
3×17×131 Posts 
I have Cullen sieve files for b=3 through b=200 for all n<1e6. If you are interested, please email 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. 
20141104, 22:09  #3 
Apr 2004
BB_{16} Posts 
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 harvey563@yahoo.com or you can message me on this forum. StevenHarvey 
20141107, 14:38  #4 
Jul 2010
Germany
101 Posts 
gc b201300
a few weeks ago i did some work for base b201300.
sieving and prptesting, and sieving is still in progress ... 
20141107, 17:35  #5 
"Mark"
Apr 2003
Between here and the
3×17×131 Posts 
What is the upper bound for your search?

20141108, 03:17  #6 
Jul 2010
Germany
101 Posts 

20141229, 18:57  #7 
"Mark"
Apr 2003
Between here and the
3·17·131 Posts 
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.

20141230, 02:02  #8 
Jul 2010
Germany
101 Posts 
i'm late. sorry!
my results for generalized cullen b=201300 to n=10e3. http://primes.ctrlxc.de/files/gc_b201300_n110e3.tar my page: http://primes.ctrlxc.de/files/primelist_testlimit i can update the if necessary 
20141230, 14:26  #9  
"Mark"
Apr 2003
Between here and the
3·17·131 Posts 
Quote:
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. 

20141230, 17:22  #10  
"Mark"
Apr 2003
Between here and the
3×17×131 Posts 
Quote:


20150202, 14:52  #11 
"Mark"
Apr 2003
Between here and the
3·17·131 Posts 
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 email 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. Last fiddled with by rogue on 20200924 at 19:47 
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