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Old 2019-04-20, 03:48   #1
kar_bon
 
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Quote:
Originally Posted by kar_bon View Post
The first attempts for Williams primes (and similiar types) are done.

The Category is shown like a portal page, perhaps this should be done on the main page later.

There're four types of Williams primes, internally differentiated by a two char coding representing the signs in the formulas (b±1)*b^n±1.
So the original Williams prime of the form (b-1)*b^n-1 are named "MM" (1st sign minus, 2nd sign minus). From this internal namings the displayed titles and the categorizations are derived.
My last search for 4*5^n-1 can be found here containing the history, external links and the Top5000 IDs in the list.

The next thing to do is to create a template to use existing data.
The basic primes should be Riesel (k*2^n-1) and Proth (k*2^n+1) types, so creating a page for the type "Williams prime PM 2" which is "(2+1)*2^n-1" or the same as "Riesel prime 3", the data from the page of the Riesel should be read and displayed on Williams page to avoid double edits.
The same for Williams 3*4^n-1 with different exponents from 3*2^n-1.
Done!

Special categories for bases without any primes found yet and a table to display all data like the Carol/Kynea primes have to be done, too.

Update:
- bases 2 to 32 are available.
- table created

ToDo:
- reusing from other types (not Riesel/Proth): example: 8*9^n-1 should use 8*3^n-1
Well, see the page https://docs.google.com/document/u/1...hdSWWWOojQ/pub, I have searched all 8 kinds of (dual) "Williams primes" for all bases b<=64 to n=3284.

Last fiddled with by kar_bon on 2020-12-02 at 01:05
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Old 2019-07-23, 20:21   #2
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Default update on 4*3^n+1 sequence

See here:
https://www.mersenneforum.org/showpo...&postcount=150

search will of course continue after I reach n=1M.

Last fiddled with by matzetoni on 2019-07-23 at 20:21
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Old 2019-08-04, 04:14   #3
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Currently Williams MM 268 was tested to n=400K with no prime found, see CRUS.

Done.

Last fiddled with by kar_bon on 2019-08-05 at 06:57 Reason: Done
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Old 2019-09-27, 16:00   #4
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See post https://mersenneforum.org/showpost.p...&postcount=760, 4*789^149139+1 is prime, you can update it to https://www.rieselprime.de/ziki/Prot..._bases_least_n
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Old 2019-10-01, 19:03   #5
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5*326^400785+1 is also prime.
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Old 2019-11-07, 20:28   #6
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Searched "Williams PP" (b+1)*b^n+1 for all 2<=b<=12^3 and 1<=n<=12^3

All numbers in this file are written in duodecimal, not including b = 1 mod 3 since for these b, all such numbers are divisible by 3

Currently, I am also running Williams MM, MP and PP for all 2<=b<=12^3 and 1<=n<=12^3
Attached Files
File Type: txt Williams PP.txt (22.2 KB, 153 views)
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Old 2019-11-07, 20:41   #7
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I also searched 2*b^n-1 (Riesel k=2), 2*b^n+1 (Proth k=2), 3*b^n-1 (Riesel k=3) and 3*b^n+1 (Proth k=3) for 2<=b<=12^3 and 1<=n<=12^3, all numbers in these text files are written in duodecimal
Attached Files
File Type: txt numbers k such that 2n^k-1.txt (38.7 KB, 165 views)
File Type: txt numbers k such that 2n^k+1.txt (24.5 KB, 158 views)
File Type: txt numbers k such that 3n^k-1.txt (21.9 KB, 148 views)
File Type: txt numbers k such that 3n^k+1.txt (22.2 KB, 156 views)
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Old 2019-11-07, 20:44   #8
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Quote:
Originally Posted by sweety439 View Post
I also searched 2*b^n-1 (Riesel k=2), 2*b^n+1 (Proth k=2), 3*b^n-1 (Riesel k=3) and 3*b^n+1 (Proth k=3) for 2<=b<=12^3 and 1<=n<=12^3, all numbers in these text files are written in duodecimal
Also 4*b^n+-1, I know that which bases have no possible prime, I don't think that the bases such that k*b^n+1 are generalized Fermat numbers should have "-" in the page https://www.rieselprime.de/ziki/Prot..._bases_least_n, since they can have primes, except the case 8*(2^7)^n+1, which has no possible prime.
Attached Files
File Type: txt numbers k such that 4n^k-1.txt (15.6 KB, 143 views)
File Type: txt numbers k such that 4n^k+1.txt (24.0 KB, 149 views)
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Old 2019-11-09, 01:29   #9
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Quote:
Originally Posted by kar_bon View Post
I'm not willing to convert duodecimal data into decimal notation!
Well, I am now finished Williams MM and Williams MP for b<=12^3 and n<=12^3, should I update these two text files to this thread?
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Old 2019-11-10, 01:22   #10
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Quote:
Originally Posted by kar_bon View Post
No, if they're in duodecimal notation. Use your blog thread then.
Well, I updated these two files for Williams MP for bases 1025<=b<=2049 (only searched to n=1024) in October, both are in decimal notation, why you deleted them?
Attached Files
File Type: txt Williams MP 1025 to 1506.txt (8.9 KB, 147 views)
File Type: txt Williams MP 1500 to 2049.txt (9.7 KB, 147 views)

Last fiddled with by sweety439 on 2019-11-10 at 01:23
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Old 2019-11-14, 11:52   #11
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Williams MM 268 has searched by CRUS to n=400K, but currently the "Notes" for the page https://www.rieselprime.de/ziki/Williams_prime_MM_least only show "Base 268: Conjectures 'R Us at 100k", it should be "Base 268: Conjectures 'R Us at 400k" (this base is only searched to 200K in the page http://harvey563.tripod.com/wills.txt), also, for Williams MM 478, R478 is started for CRUS: see post https://mersenneforum.org/showpost.p...postcount=1983
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