Generalized Cullen / Woodall Coordinated Search - Reservations/Status
 

The history and status for Generalized Cullens has been moved from [URL="http://www.loeh.name/guenter/gc/"]here[/URL] to [URL="https://www.rieselprime.de/ziki/Cullen_prime_table"]the Prime Wiki[/URL]. Guenter Loeh's webpage hasn't been updated in over three years and e-mails have gone unanswered.

The history and status for Generalized Woodall's has been moved from [URL="https://harvey563.tripod.com/"]here[/URL] to [URL="https://www.rieselprime.de/ziki/Woodall_prime_table"]the Prime Wiki[/URL]. These haven't been updated in a while either. I have communicated with Steven Harvey and he welcomes this change. Outside of the Carol/Kynea forms the other searches he has maintained have not been moved.

At this point all bases <= 50 have been added to those pages as well as a smattering of other bases. The next goal is to get all bases <= 100 on those pages. Steven Harvey's site has data for all bases (both Cullen and Woodall) to b <= 10000. Eventually that will be on the Prime Wiki as well.

Unfortunately there is insufficient detail on Guenther's site regarding the history of searching of the bases. I made the assumption that the limits from his website are accurate and used those on the Prime Wiki.

This thread is for the coordination of reservations. If you reserve a base not on the Prime Wiki, one will be created.

You can sieve these forms efficiently with gcwsieve and gcwsievecl (available [URL="https://sourceforge.net/projects/mtsieve/"]here[/URL]). You can do PRP/primality testing with llr, llr2, and pfgw.

The Top 20 Generalized Cullen primes can be found [URL="https://t5k.org/top20/page.php?id=42"]here[/URL].

The Top 20 Generalized Woodall primes can be found [URL="https://t5k.org/top20/page.php?id=45"]here[/URL].

I am reserving Cullen bases 15, 16, 22, 23, 24, 26, 30, 31, 32, 33, 34, 35, 36, 38, 40, 42, 43, 44, 45, 46, 48, and 50. This will start as a double-check with the intention of testing these bases up to n=200000. None of these have been searched to that n so there should be a few discoveries in the range, but nothing that is Top 5000.

I'd like to reserve the generalized Woodalls [URL="https://www.rieselprime.de/ziki/Woodall_prime_table"]here[/URL] with bases 10..20 (inclusive) to n=1M each.

Please be aware that I am running base 11 as I have been stated previously.

[QUOTE=kruoli;627675]Please be aware that I am running base 11 as I have been stated previously.[/QUOTE]

Sorry, I missed that. I will skip b=11 for the Woodalls.

I will handle b=7 for the Woodalls up to n=500k, including double checking the range already searched.

hi,
reserving b=101 for woodall

Playing with b=202 for Cullen ( not edward)

already found one prime for n=28968

28968*202^28968+1 is 3-PRP! (28.3668s+0.0005s) 66786 digits

[QUOTE=firejuggler;628310]Playing with b=202 for Cullen ( not edward)

already found one prime for n=28968

28968*202^28968+1 is 3-PRP! (28.3668s+0.0005s) 66786 digits[/QUOTE]

Thanks !
[url]https://pzktupel.de/Primetables/TableCullenGEN.php[/url]

[QUOTE=firejuggler;628310]Playing with b=202 for Cullen ( not edward)

already found one prime for n=28968

28968*202^28968+1 is 3-PRP! (28.3668s+0.0005s) 66786 digits[/QUOTE]

Have you confirmed that 28968*202^28968+1 is the smallest Cullen prime to base 202? [URL="https://harvey563.tripod.com/GClist.txt"]Harvey's page[/URL] shows that there is no Cullen prime to base 202 with n<=10000

(BTW, your result shows that every even base < 254 except base 146 has at least one known Cullen prime, if n>=b-1 is not required)

I have only checked above 10k, but should be easy to check n=201 to 10k


edit : reverified, no prime below 10k