mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > sweety439

Reply
 
Thread Tools
Old 2020-06-20, 02:13   #826
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

22·7·317 Posts
Default

Quote:
Originally Posted by Uncwilly View Post
what is your reason for quoting huge blocks of text that you posted on the same day?
Hanlon's Razor
LaurV is offline   Reply With Quote
Old 2020-06-21, 13:40   #827
sweety439
 
sweety439's Avatar
 
Nov 2016

2×3×5×79 Posts
Default

update newest files
Attached Files
File Type: txt first 16 Sierpinski CK.txt (26.4 KB, 13 views)
File Type: txt first 16 Riesel CK.txt (26.4 KB, 14 views)
sweety439 is offline   Reply With Quote
Old 2020-06-22, 23:00   #828
sweety439
 
sweety439's Avatar
 
Nov 2016

2·3·5·79 Posts
Default

Update zip files for 1st, 2nd, and 3rd conjectures for bases <= 32 (except 2, 3, 6, 15, 22, 24, 28, 30) and bases 64, 128, 256
Attached Files
File Type: zip 1st, 2nd, and 3rd conjectures.zip (79.2 KB, 14 views)
sweety439 is offline   Reply With Quote
Old 2020-06-24, 23:56   #829
sweety439
 
sweety439's Avatar
 
Nov 2016

2×3×5×79 Posts
Default

Update files.
Attached Files
File Type: txt conjectured first 4 Sierpinski numbers.txt (6.2 KB, 12 views)
File Type: txt conjectured first 4 Riesel numbers.txt (6.2 KB, 14 views)
sweety439 is offline   Reply With Quote
Old 2020-06-25, 00:02   #830
sweety439
 
sweety439's Avatar
 
Nov 2016

45028 Posts
Default

Extended to base 539

Note: I only searched the k <= 5000000, if there are <16 Sierpinski/Riesel k's <= 5000000, then this text file only show the Sierpinski/Riesel k's <= 5000000 for this Sierpinski/Riesel base (if there are no Sierpinski/Riesel k's <= 5000000, then this text file do not show any Sierpinski/Riesel k's <= 5000000 for this Sierpinski/Riesel base), also, I only searched the exponent n <= 2000 (for (k*b^n+-1)/gcd(k+-1,b-1), + for Sierpinski, - for Riesel) and only searched the primes <= 100000 (for the prime factor of (k*b^n+-1)/gcd(k+-1,b-1), + for Sierpinski, - for Riesel), thus this text file wrongly shows 1 as Sierpinski number base 125, although (1*125^n+1)/gcd(1+1,125-1) has no covering set, but since (1*125^n+1)/gcd(1+1,125-1) has a prime factor <= 100000 for all n <= 2000
Attached Files
File Type: txt first 16 Sierpinski CK.txt (46.2 KB, 15 views)
File Type: txt first 16 Riesel CK.txt (46.1 KB, 14 views)

Last fiddled with by sweety439 on 2020-06-25 at 00:05
sweety439 is offline   Reply With Quote
Old 2020-06-25, 07:19   #831
sweety439
 
sweety439's Avatar
 
Nov 2016

2·3·5·79 Posts
Default

This project is from CRUS, extended to the k such that gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not 1. Since k*b^n+-1 is always divisible by gcd(k+-1,b-1), it is to simply take out this factor and find and prove the smallest value of k for (k*b^n+-1)/gcd(k+-1,b-1) which is 'Sierpinski value' (+1 form) or 'Riesel value' (-1 form) that is not prime for all values of n >= 1.

Last fiddled with by sweety439 on 2020-06-25 at 07:22
sweety439 is offline   Reply With Quote
Old 2020-06-25, 07:19   #832
sweety439
 
sweety439's Avatar
 
Nov 2016

2×3×5×79 Posts
Default

Sierpinski problem base b: Finding and proving the smallest k such that gcd(k+1,b-1)=1 and k*b^n+1 is not prime for all integers n>=1.

Riesel problem base b: Finding and proving the smallest k such that gcd(k-1,b-1)=1 and k*b^n-1 is not prime for all integers n>=1.

Extended Sierpinski problem base b: Finding and proving the smallest k such that (k*b^n+1)/gcd(k+1,b-1) is not prime for all integers n>=1.

Extended Riesel problem base b: Finding and proving the smallest k such that (k*b^n-1)/gcd(k-1,b-1) is not prime for all integers n>=1.

With this effort, we aim to prove many of the Riesel and Sierpinski conjectures for bases <= 128 and bases 256, 512, 1024.

Project definition:

For every base (b) for the forms (k*b^n+1)/gcd(k+1,b-1) and (k*b^n-1)/gcd(k-1,b-1), there exists a unique value of k for each form that has been conjectured to be the lowest 'Sierpinski value' (+1 form) or 'Riesel value' (-1 form) that is composite for all values of n >= 1.

Goal:

Prove the conjectures by finding at least one (probable) prime (if only PRP, prove its primality) for all lower values of k. Many of the conjectures have already been proven but much more work is needed to prove additional bases. Proving them all is not possible but we aim to prove many of them.

There are many conjectures where only ONE k needs a (probable) prime (and many more that need only two). If you find it, you could be the one to prove a conjecture! This is a big deal to us here.
Algebraic factors have been found for many k's, which prove them composite for all n, allowing them to be removed from searches.
Notes:

All n must be >= 1.

k-values that make a full covering set with all or partial algebraic factors are excluded from the conjectures.

k-values that are a multiple of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime are included in the conjectures but excluded from testing. Such k-values will have the same prime as k / b.

See "table of Riesel problems.txt" and "table of Sierpinski problems.txt" for:

The covering set of the conjectured k for each Sierpinski/Riesel base.
The k's that make a full covering set with all or partial algebraic factors for each Sierpinski/Riesel base.
The remaining k's to find prime for each Sierpinski/Riesel base.
The top 10 k's with largest first primes for each Sierpinski/Riesel base.
This project is to solve the Sierpinski/Riesel conjectures for bases b <= 128 and bases b = 256, 512, 1024. (this project will be extended to bases b <= 2048 in future)
sweety439 is offline   Reply With Quote
Old 2020-06-25, 21:25   #833
sweety439
 
sweety439's Avatar
 
Nov 2016

2×3×5×79 Posts
Default

Original CRUS project definition:

For every base (b) for the forms k*b^n+1 and k*b^n-1, there exists a unique value of k for each form that has been conjectured to be the lowest 'Sierpinski value' (+1 form) or 'Riesel value' (-1 form) that is not prime for all values of n >= 1. k's that have a trivial factor (one factor the same) for all n-values (this trivial factor is gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel)) are not considered. (Thus, only the k's such that gcd(k+-1,b-1) = 1 are considered) The project is finding and proving this value of k.

This project extends the original CRUS project to the k's such that gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not 1. For these k's, we can deal with the fact that k*b^n+-1 is always divisible by gcd(k+-1,b-1), it is to simply take out this factor and find and prove the value of k for each form that has been conjectured to be the lowest 'Sierpinski value' (+1 form) or 'Riesel value' (-1 form) that is not prime for all values of n >= 1.

Goal:

Prove the conjectures for bases b<=2048 by finding at least one (probable) prime (if only PRP, prove its primality) for all lower values of k. Many of the conjectures have already been proven but much more work is needed to prove additional bases. Proving them all is not possible but we aim to prove many of them.

Notes:

All n must be >= 1.

k-values that make a full covering set with all or partial algebraic factors are excluded from the conjectures.

k-values that are a multiple of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime are included in the conjectures but excluded from testing. Such k-values will have the same prime as k / b.
sweety439 is offline   Reply With Quote
Old 2020-06-25, 21:27   #834
sweety439
 
sweety439's Avatar
 
Nov 2016

2·3·5·79 Posts
Default

Ranges:

k >= 1

b >= 2

n >= 1
sweety439 is offline   Reply With Quote
Old 2020-06-25, 21:29   #835
sweety439
 
sweety439's Avatar
 
Nov 2016

45028 Posts
Default

Since these conjectures extend to the k such that gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not 1, so these conjectures are called extended Sierpinski/Riesel conjectures base b
sweety439 is offline   Reply With Quote
Old 2020-06-26, 01:31   #836
sweety439
 
sweety439's Avatar
 
Nov 2016

2×3×5×79 Posts
Default

The 1st, 2nd, 3rd, and 4th conjectures for Sierpinski/Riesel bases <=64 and 128 and 256 with smaller conjectures
Attached Files
File Type: zip first 4 SR conjectures.zip (121.3 KB, 14 views)
sweety439 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Semiprime and n-almost prime candidate for the k's with algebra for the Sierpinski/Riesel problem sweety439 sweety439 11 2020-09-23 01:42
The reverse Sierpinski/Riesel problem sweety439 sweety439 20 2020-07-03 17:22
The dual Sierpinski/Riesel problem sweety439 sweety439 12 2017-12-01 21:56
Sierpinski/ Riesel bases 6 to 18 robert44444uk Conjectures 'R Us 139 2007-12-17 05:17
Sierpinski/Riesel Base 10 rogue Conjectures 'R Us 11 2007-12-17 05:08

All times are UTC. The time now is 08:50.

Fri Oct 30 08:50:26 UTC 2020 up 50 days, 6:01, 1 user, load averages: 2.00, 1.93, 1.81

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.