[QUOTE=sweety439;519877]If a prime in the list is also other classes of primes, I think it should be in the notes, like the article [URL="https://www.rieselprime.de/ziki/Riesel_prime_3"]Riesel 3[/URL], ...[/QUOTE]

Sorry for not including hundreds of years of prime searching in a 6 months running Wiki and having a real life, too but only (here on earth) 24 hours a day to work on such pages.

[QUOTE=kar_bon;519881]Sorry for not including hundreds of years of prime searching in a 6 months running Wiki and having a real life, too but only (here on earth) 24 hours a day to work on such pages.[/QUOTE]

However, ALL [URL="https://www.rieselprime.de/ziki/Williams_prime_MP_5"]Williams MP 5[/URL] are also [URL="https://primes.utm.edu/top20/page.php?id=12"]Generalized Fermat primes[/URL], but only "20462" and "70130" has this note.

[QUOTE=sweety439;519888]However, ALL [URL="https://www.rieselprime.de/ziki/Williams_prime_MP_5"]Williams MP 5[/URL] are also [URL="https://primes.utm.edu/top20/page.php?id=12"]Generalized Fermat primes[/URL], but only "20462" and "70130" has this note.[/QUOTE]

Posting over and over again the same isn't of any help. I only used the comments from the Top5000 entries there. I also have to determine the best way how to put those many different prime type you mentioned in the comments of any n-value of any base and prime type.

In the page [URL="https://www.rieselprime.de/ziki/Williams_prime"]Williams prime[/URL], the "Available Online Sequences" section only lists 2<=b<=10, however, currently Williams MM has available OEIS sequences for all 2<=b<=14, and Williams MP has available OEIS sequences for all 3<=b<=12 (with the exception of b=4).

Also, currently Cullen has available OEIS sequences for all 2<=b<=18 (with the exception of b=5, b=11, b=13 and b=17), and Woodall has available OEIS sequences for all 2<=b<=20.

There are also OEIS sequences:

Smallest Williams MP: A305531
Smallest Cullen: A240234
Smallest Woodall: A240235

@kar_bon, you missed a sequence: Williams PP 171, it also has no primes with exponent n<=1024.

[COLOR="Green"]Done.[/COLOR]

I've generated a template for showing [URL="https://www.rieselprime.de/ziki/Template:HistS"]the history of sieve files.
[/URL]
This template could be useful for the CRUS sequences as well as projects like the Carol/Kynea search.
Calling is fairly simple: there are 5 parameters (date, upper range, contributors, lower range and post), of which the last 2 are optional.
If the 4th parameter is not given, it is assumed that the file starts from 1.

Thanks, I've changed the template a little bit.

No need to give the range start as separate parameter, range given at all, so this template is more than the others in handling parameters: date, param(mostly), contributor, post ID(optional).

I also added this entry to CK50.

I've created an alternate table for [url='https://www.rieselprime.de/ziki/Carol-Kynea_table_alternate']Carol/Kynea[/url]:
- no sieve files listed
- no contributors listed
- n-values listed in one line (mostly sufficient)

Done so far:
- all (hope so) available historical data from
-- 3 threads in this forum
-- old page from S.Harvey
-- some old Yahoo posts

(A short table for copying the data into an editor is available [url='https://www.rieselprime.de/ziki/Carol-Kynea_table_short']here[/url].)

Links see [url='https://www.rieselprime.de/ziki/Carol-Kynea_prime']here[/url], this page has to be updated after the following is done:

- [STRIKE]some bases without Carol or Kynea to insert[/STRIKE] [COLOR="Green"]Done[/COLOR]. For all bases <= 3000 there are currently
-- [url='https://www.rieselprime.de/ziki/Category:Carol-Kynea_without_Carol']96 without[/url] a Carol prime
-- [url='https://www.rieselprime.de/ziki/Category:Carol-Kynea_without_Kynea']78 without[/url] a Kynea prime
- remaining data for bases<=3000 from my page/search
- two tables with least Carol or Kynea n-value

If more bases will be filled in it's better to change the template for categorizing any base into different parts (like 1-999, 1000-1999, 2000-2999,...).

Nice to have:
- some statistics
- some graphs

[B]History entries[/B] and reserving any base (see [url='https://www.rieselprime.de/ziki/Carol-Kynea_prime_2']base 2[/url] for example) are also available as well as inserting a [B]sieve file[/B] (see [url='https://www.rieselprime.de/ziki/Carol-Kynea_prime_50']base 50[/url]).
The same procedure can be done for other prime types.

For Leyland primes, why the pages are "Leyland_prime P x y" and "Leyland_prime M x y" (a page for a single (probable) prime)? Not "Leyland_prime P x" and "Leyland_prime M x" (list all y's such that x^y+y^x or |x^y-y^x| are (probable) primes)? Like the pages for Williams primes and the Carol/Kynea primes and the Cullen/Woodall primes? e.g. for the Carol/Kynea primes, the pages list all n such that (b^n-1)^2-2 or (b^n+1)^2-2 are primes for a fixed b, why not (for Leyland primes) list all y such that x^y+y^x or |x^y-y^x| are (probable) primes for a fixed x?

[QUOTE=sweety439;522174]For Leyland primes, why the pages are "Leyland_prime P x y" and "Leyland_prime M x y" (a page for a single (probable) prime)?[/QUOTE]

Those numbers are more individual than Carol/Kynea. Finder/prover and dates are more different.
On the other hand most of those numbers (not yet all of more than 1400) are with different x-/y-values so most categories as "Leyland_prime P x" would contain only one member. This is not very clear and a table is also harder to create.

If you want such list, sorting the table by x- or y-value you get this.