Odds of prime discussion - Page 3

TheCount · 2013-10-27, 09:19

Quote:

Originally Posted by henryzz

In this kind of spreadsheet formula simplification of that form isn't necessary. I would prefer the accuracy myself.

Your right. I'd use the full equation in a spreadsheet situation.

I am working on probabilities for the 2k's.
I've been checking P1e6 weights and I got different values compared to column "n per 25000 at 1e12"/1.25 in the "Unproven Conjectures" table for these Bases:
R463, R696, R774, R588, R828, S140, S533
I've been using >srsieve -n 100001 -N 110000 -P 1e6 equation_file.txt
Where equation_file.txt has the equation with each k on a separate line.
All the other 83 2k's bases matched.
Maybe there's an error in the scripts?

gd_barnes · 2013-10-27, 09:42

Quote:

Originally Posted by TheCount

Your right. I'd use the full equation in a spreadsheet situation.

I am working on probabilities for the 2k's.
I've been checking P1e6 weights and I got different values compared to column "n per 25000 at 1e12"/1.25 in the "Unproven Conjectures" table for these Bases:
R463, R696, R774, R588, R828, S140, S533
I've been using >srsieve -n 100001 -N 110000 -P 1e6 equation_file.txt
Where equation_file.txt has the equation with each k on a separate line.
All the other 83 2k's bases matched.
Maybe there's an error in the scripts?

Are you using the latest version of srsieve? All of these bases have k's that are perfect squares (Riesel) or perfect cubes (Riesel & Sierp). Where the k is a perfect square, all n==(0 mod 2) are removed and where k is a perfect cube, all n==(0 mod 3) are removed due to algebraic factors. The latest version of srsieve takes this into account.

That is one thing that Mark and I checked closely and we went through a couple of rounds of corrections when the pages were implemented.

We do appreciate any kind of error checking by anyone anywhere on the web pages or 1st postings in several of our threads. There are a large number of things that have to remain synced up and usually at some point, errors and inconsistencies will creep in.

TheCount · 2013-10-27, 12:53

I was using srsieve_0.6.17 which has been the latest version since May 31, 2010 as far as I can tell.
Yes all these bases have one or two k being a perfect cube or square.
Does srsieve need some special flag to take account of perfect cubes or squares?
Or do I need to do another step before/after using srsieve?
For R463:
>srsieve -n 100001 -N 110000 -P 1e6 "216*463^n-1", I get 269 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "356*463^n-1", I get 252 terms remaining
For R696:
>srsieve -n 100001 -N 110000 -P 1e6 "152*696^n-1", I get 705 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "225*696^n-1", I get 1014 terms remaining
For R774:
>srsieve -n 100001 -N 110000 -P 1e6 "25*774^n-1", I get 671 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "30*774^n-1", I get 447 terms remaining
For R588:
>srsieve -n 100001 -N 110000 -P 1e6 "3*588^n-1", I get 795 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "16*588^n-1", I get 664 terms remaining
For R828:
>srsieve -n 100001 -N 110000 -P 1e6 "64*828^n-1", I get 404 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "68*828^n-1", I get 676 terms remaining
For S140:
>srsieve -n 100001 -N 110000 -P 1e6 "8*140^n+1", I get 328 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "16*140^n+1", I get 642 terms remaining
For S533:
>srsieve -n 100001 -N 110000 -P 1e6 "38*533^n+1", I get 747 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "64*533^n+1", I get 691 terms remaining
The values I get are always higher, so it's consistent that more factors needing to be eliminated.

Keeping on top of all these conjectures is a really big task and you and others obviously put in a massive effort.
I am sure everyone appreciates it.

TheCount · 2013-10-28, 04:46

Splitting into a separate thread was a good idea. I was getting offtrack from 1k's.

I got hold of srsieve v 1.0.7 and it provides the correct factors remaining for those bases with perfect cubes or squares.

My next question is should we be using srsieve_1.0.7 or the srsieve_0.6.17 that comes in the CRUS Pack for prime-search efforts for the conjectures?

gd_barnes · 2013-10-28, 05:06

Quote:

Originally Posted by TheCount

My next question is should we be using srsieve_1.0.7 or the srsieve_0.6.17 that comes in the CRUS Pack for prime-search efforts for the conjectures?

The latest version has shown to be bug free. You can use it.

TheCount · 2013-11-03, 02:11

I've done the probabilities for the 3k's.
I am going to put the results on a web page.

I checked the P1e6 weights and I got different values for R814 (k=14,44,128) and R298 (k=27,92,105).
I am using srsieve v 1.0.7 so cubes etc. should be taken care of.

For R814:
>srsieve -n 100001 -N 110000 -P 1e6 "14*814^n-1", I get 522 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "44*814^n-1", I get 869 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "128*814^n-1", I get 964 terms remaining
Adds up to 2355 but expected total 2305 based on "Unproven Conjectures" table.

For R298:
>srsieve -n 100001 -N 110000 -P 1e6 "27*298^n-1", I get 279 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "92*298^n-1", I get 297 terms remaining
>srsieve -n 100001 -N 110000 -P 1e6 "105*298^n-1", I get 735 terms remaining
Adds up to 1311 but expected total 1276 based on "Unproven Conjectures" table.

All the other 2 and 3k's match.

TheCount · 2014-08-17, 22:38

I've updated my chance spreadsheet after the recent large update by Gary.
I was posting on a webpage with Wix, but its very fiddly and time consuming. Wix does not support tables well. So decided to just post the spreadsheet instead.

A few notes about the CRUS spreadsheet:
Shading shows reservation, same as the CRUS website.
1k's, 2k's, 3k's, 4k's and 13k's chances are calculated.
The "Next Test End Range" is 100k more than the current "Test Limit" but you can set this to whatever you like.
Best chance for a S/R k is highlighted yellow.
For >1k's I also calculate the chance any of the k's will be prime and the chance of all the k's being primed in the next test range.
The error column is a check of the Weight against the CRUS website value. Shaded Salmon colour if it doesn't match.
For the 1k's I also calculate the chance using the Nash weight (sieve for n=100001 to 110000 to P=511) in columns R, S, T.
In columns U to AB I also calculate the chance the same way as the "odds of prime" spreadsheet. Only one in 5 of the 1k's are currently sieved to make a comparison.
For the 19 1k's where we have all 3 chance values it appears that the deeper you sieve the more the chance value seems to approach an asymptote, i.e. the more work you do to refine your chance value the more accurate it will be.

LaurV · 2014-08-18, 03:01

[offtopic] Excel Tips (I consider myself an Excel Expert :P)
you can use the "count" function (no pun intended

) and get rid of the last two columns; also get rid of the two empty spreadsheets, etc. and few other tricks, then the size of the file is about half. Which is good when you attach files to a forum like this with limited quota.
[/offtopic]

TheCount · 2014-09-08, 15:26

"count" function! Hha Ha ha

Yes is trivial. I use Open Office so I don't pay an MS tax for every install. Using count function and removing tabs with Open Office doesn't materially reduce the file size for me. I posted a zipped version. I think its worth the quota.

Look up "The Count Censored" on You Tube for a laugh.

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2013-10-27, 12:53	#25
TheCount Sep 2013 Perth, Au. 142₈ Posts	I was using srsieve_0.6.17 which has been the latest version since May 31, 2010 as far as I can tell. Yes all these bases have one or two k being a perfect cube or square. Does srsieve need some special flag to take account of perfect cubes or squares? Or do I need to do another step before/after using srsieve? For R463: >srsieve -n 100001 -N 110000 -P 1e6 "216463^n-1", I get 269 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "356463^n-1", I get 252 terms remaining For R696: >srsieve -n 100001 -N 110000 -P 1e6 "152696^n-1", I get 705 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "225696^n-1", I get 1014 terms remaining For R774: >srsieve -n 100001 -N 110000 -P 1e6 "25774^n-1", I get 671 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "30774^n-1", I get 447 terms remaining For R588: >srsieve -n 100001 -N 110000 -P 1e6 "3588^n-1", I get 795 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "16588^n-1", I get 664 terms remaining For R828: >srsieve -n 100001 -N 110000 -P 1e6 "64828^n-1", I get 404 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "68828^n-1", I get 676 terms remaining For S140: >srsieve -n 100001 -N 110000 -P 1e6 "8140^n+1", I get 328 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "16140^n+1", I get 642 terms remaining For S533: >srsieve -n 100001 -N 110000 -P 1e6 "38533^n+1", I get 747 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "64533^n+1", I get 691 terms remaining The values I get are always higher, so it's consistent that more factors needing to be eliminated. Keeping on top of all these conjectures is a really big task and you and others obviously put in a massive effort. I am sure everyone appreciates it.

2013-10-28, 04:46	#26
TheCount Sep 2013 Perth, Au. 2·7² Posts	Splitting into a separate thread was a good idea. I was getting offtrack from 1k's. I got hold of srsieve v 1.0.7 and it provides the correct factors remaining for those bases with perfect cubes or squares. My next question is should we be using srsieve_1.0.7 or the srsieve_0.6.17 that comes in the CRUS Pack for prime-search efforts for the conjectures?

2013-11-03, 02:11	#28
TheCount Sep 2013 Perth, Au. 2×7² Posts	I've done the probabilities for the 3k's. I am going to put the results on a web page. I checked the P1e6 weights and I got different values for R814 (k=14,44,128) and R298 (k=27,92,105). I am using srsieve v 1.0.7 so cubes etc. should be taken care of. For R814: >srsieve -n 100001 -N 110000 -P 1e6 "14814^n-1", I get 522 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "44814^n-1", I get 869 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "128814^n-1", I get 964 terms remaining Adds up to 2355 but expected total 2305 based on "Unproven Conjectures" table. For R298: >srsieve -n 100001 -N 110000 -P 1e6 "27298^n-1", I get 279 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "92298^n-1", I get 297 terms remaining >srsieve -n 100001 -N 110000 -P 1e6 "105298^n-1", I get 735 terms remaining Adds up to 1311 but expected total 1276 based on "Unproven Conjectures" table. All the other 2 and 3k's match.

2014-08-18, 03:01	#30
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 10011011101001₂ Posts	[offtopic] Excel Tips (I consider myself an Excel Expert :P) you can use the "count" function (no pun intended ) and get rid of the last two columns; also get rid of the two empty spreadsheets, etc. and few other tricks, then the size of the file is about half. Which is good when you attach files to a forum like this with limited quota. [/offtopic]

2014-09-08, 15:26	#31
TheCount Sep 2013 Perth, Au. 2·7² Posts	"count" function! Hha Ha ha Yes is trivial. I use Open Office so I don't pay an MS tax for every install. Using count function and removing tabs with Open Office doesn't materially reduce the file size for me. I posted a zipped version. I think its worth the quota. Look up "The Count Censored" on You Tube for a laugh.