mersenneforum.org Do not post your results here!
 Register FAQ Search Today's Posts Mark Forums Read

2019-04-20, 03:48   #1
kar_bon

Mar 2006
Germany

2,999 Posts
Do not post your results here!

This thread is for results posted in this subforum but should belong to their own topics!

DO NOT POST YOUR RESULTS HERE!

---------------------------------------------------------------------------------------------------------------------------------

Quote:
 Originally Posted by kar_bon 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

 2019-07-23, 20:21 #2 matzetoni     Feb 2019 97 Posts 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
 2019-08-04, 04:14 #3 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2·7·263 Posts 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
 2019-09-27, 16:00 #4 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2×7×263 Posts 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
 2019-10-01, 19:03 #5 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 71428 Posts 5*326^400785+1 is also prime.
2019-11-07, 20:28   #6
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

E6216 Posts

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
 Williams PP.txt (22.2 KB, 178 views)

2019-11-07, 20:41   #7
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

2·7·263 Posts

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
 numbers k such that 2n^k-1.txt (38.7 KB, 218 views) numbers k such that 2n^k+1.txt (24.5 KB, 213 views) numbers k such that 3n^k-1.txt (21.9 KB, 197 views) numbers k such that 3n^k+1.txt (22.2 KB, 209 views)

2019-11-07, 20:44   #8
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

2×7×263 Posts

Quote:
 Originally Posted by sweety439 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
 numbers k such that 4n^k-1.txt (15.6 KB, 195 views) numbers k such that 4n^k+1.txt (24.0 KB, 199 views)

2019-11-09, 01:29   #9
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

2×7×263 Posts

Quote:
 Originally Posted by kar_bon 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?

2019-11-10, 01:22   #10
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

2×7×263 Posts

Quote:
 Originally Posted by kar_bon 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
 Williams MP 1025 to 1506.txt (8.9 KB, 199 views) Williams MP 1500 to 2049.txt (9.7 KB, 199 views)

Last fiddled with by sweety439 on 2019-11-10 at 01:23

 2019-11-14, 11:52 #11 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2·7·263 Posts 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

 Similar Threads Thread Thread Starter Forum Replies Last Post swellman NFS@Home 544 2020-12-31 15:14 swellman NFS@Home 112 2020-12-29 22:58 pinhodecarlos NFS@Home 551 2019-01-04 13:06 James Heinrich PrimeNet 2 2011-01-21 20:42 jasong Octoproth Search 3 2007-06-10 21:08

All times are UTC. The time now is 10:23.

Sun Feb 5 10:23:18 UTC 2023 up 171 days, 7:51, 1 user, load averages: 0.51, 0.72, 0.73