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Search: Posts Made By: paulunderwood
Forum: Miscellaneous Math 2020-08-03, 19:36
Replies: 75
Views: 5,627
Posted By paulunderwood
Thumbs down House of cards

[n,b] = [79786523, 2982537] is a counterexample to the test given in post #74 where r=1. This was overlooked because of the same programming error indicated in post #75. The only thing to be lifted...
Forum: Miscellaneous Math 2020-08-03, 14:20
Replies: 75
Views: 5,627
Posted By paulunderwood
w00t 1+1 selfridges

Here is a 1+1 selfridges algorithm:

Given a non-square n find b:


kronecker(b,n)==1
kronecker(1-b,n)==-1
gcd(4-b,n)==1
gcd(4-2*b,n)==1
Forum: Miscellaneous Math 2020-08-02, 09:15
Replies: 75
Views: 5,627
Posted By paulunderwood
Cool Second draft

:book: :mooc:
Forum: Proth Prime Search 2020-07-31, 22:23
Replies: 158
Views: 35,125
Posted By paulunderwood
Congratulations for a top 20 prime!

Congratulations for a top 20 prime!
Forum: Programming 2020-07-31, 11:03
Replies: 53
Views: 7,965
Posted By paulunderwood
Arrow Here is a gwnum program that tests...

Here is a gwnum program that tests Euler+Frobenius as per https://mersenneforum.org/showpost.php?p=552286&postcount=74. :fish1:
Forum: PARI/GP 2020-07-30, 13:56
Replies: 12
Views: 328
Posted By paulunderwood
?solve solve(X=a,b,expr): real root of...

?solve
solve(X=a,b,expr): real root of expression expr (X between a and b), where
expr(a)*expr(b)<=0.


For logarithmic equations use pen and paper and an internet search engine.
Forum: Miscellaneous Math 2020-07-30, 01:10
Replies: 75
Views: 5,627
Posted By paulunderwood
Red face Answer and warning

Apart form the ill-formed question, writing b=s^2 (and found by trial and error) the answer is:

(x*(1-s^2))^((n+1)/2) == s*(1-s^2)*kronecker(2*(1-s),n) (mod n, x^2-2*x+s^2),

Warning: this...
Forum: Linux 2020-07-29, 04:04
Replies: 13
Views: 400
Posted By paulunderwood
This looks like a problem with unattended...

This looks like a problem with unattended upgrades. Remove it (https://ostechnix.com/how-to-disable-unattended-upgrades-on-ubuntu/) with sudo apt remove unattended-upgrades or disable it via sudo...
Forum: Linux 2020-07-29, 03:31
Replies: 13
Views: 400
Posted By paulunderwood
This...

This (https://serverfault.com/questions/884597/how-to-find-reason-for-system-reboot-or-shutdown-in-ubuntu-16-04-system) says run the command egrep -ir "(shut|reboot)" /var/log/*
Forum: Linux 2020-07-29, 02:58
Replies: 13
Views: 400
Posted By paulunderwood
Freshly installed Debian has to be coaxed into...

Freshly installed Debian has to be coaxed into not suspending (https://wiki.debian.org/Suspend#Disable_suspend_and_hibernation) etc after ~20 minutes with a mask command. I wonder if your problem is...
Forum: Miscellaneous Math 2020-07-28, 18:53
Replies: 75
Views: 5,627
Posted By paulunderwood
Question Simplification

Recap: The solutions to x^2-2^r*x+b=0 are x=2^(r-1)+-sqrt(4^(r-1)-b).

Let r=1. Then the solutions are to the equation x^2-2*x+b=0 which are x=1+-sqrt(1-b)

We have to have kronecker(1-b,n)==-1,...
Forum: Miscellaneous Math 2020-07-28, 02:05
Replies: 75
Views: 5,627
Posted By paulunderwood
Forum: Miscellaneous Math 2020-07-27, 14:23
Replies: 75
Views: 5,627
Posted By paulunderwood
Cool most general test (revised)

I found some counterexamples to the above.

The revised test:


b%n!=0
!issquare(n)
gcd(a^2-b,n)==1
gcd(a^2-2*b,n)==1
gcd(a^2-3*a,n)==1
Forum: Miscellaneous Math 2020-07-27, 11:51
Replies: 75
Views: 5,627
Posted By paulunderwood
To fool 2-PSPs and Carmichael numbers lists...

To fool 2-PSPs and Carmichael numbers lists gcd(a^2-3*b,n)==1 is also required. :cool:
Forum: Miscellaneous Math 2020-07-27, 10:15
Replies: 75
Views: 5,627
Posted By paulunderwood
most general test

Let x^2-a*x+b=0. The solutions are x=a/2 +- sqrt(a^2-4*b)/2.

The test is:


b%n!=0
!issquare(n)
gcd(a^2-b,n)==1
gcd(a^2-2*b,n)==1
kronecker(a^2-4*b,n)==-1
Forum: GpuOwl 2020-07-26, 15:06
Replies: 13
Views: 581
Posted By paulunderwood
Aha! I have to do the manual results submission...

Aha! I have to do the manual results submission in order to enable upload, so it seems.
Forum: GpuOwl 2020-07-26, 11:52
Replies: 13
Views: 581
Posted By paulunderwood
Uploading ability seems to be intermittent. 401...

Uploading ability seems to be intermittent. 401 error. I will try later. :smile:
Forum: Wagstaff PRP Search 2020-07-25, 15:49
Replies: 4
Views: 1,912
Posted By paulunderwood
Consider x^2-2*x-1=0. This has solutions x= 1 +-...

Consider x^2-2*x-1=0. This has solutions x= 1 +- sqrt(2). But 2^((W-1)/2) == -1 mod W where W=(2^p+1)/3 because kronecker(2,W) == -1. I propose the test:

Mod(Mod(1,W)*x,x^2-2*x-1)^(W+1)==-1 for...
Forum: Marin's Mersenne-aries 2020-07-25, 04:01
Replies: 36
Views: 1,098
Posted By paulunderwood
Maybe v30 should be called Prime10 :grin:

Maybe v30 should be called Prime10 :grin:
Forum: GpuOwl 2020-07-25, 00:35
Replies: 13
Views: 581
Posted By paulunderwood
Uploading seems to work now for the old proof...

Uploading seems to work now for the old proof result format.
Forum: PrimeNet 2020-07-24, 15:01
Replies: 45
Views: 5,224
Posted By paulunderwood
Ben is doing over 10x the first time tests...

Ben is doing over 10x the first time tests (https://www.mersenne.org/report_top_500_ll/) of Curtis "Chuck Norris" Cooper atm :flex:
Forum: GpuOwl 2020-07-24, 12:05
Replies: 13
Views: 581
Posted By paulunderwood
Compiled well. :smile: Edit: Uploading...

Compiled well. :smile:

Edit: Uploading requires the new format :tu:
Forum: GpuOwl 2020-07-24, 10:08
Replies: 13
Views: 581
Posted By paulunderwood
Two problems: 1. I can't compile the latest...

Two problems:

1. I can't compile the latest gpuOwl:

make gpuowl
echo \"`git describe --long --dirty --always`\" > version.new
diff -q -N version.new version.inc >/dev/null || mv version.new...
Forum: Mlucas 2020-07-22, 21:50
Replies: 116
Views: 8,249
Posted By paulunderwood
According to this page...

According to this page (https://www.hardkernel.com/shop/odroid-n2-with-4gbyte-ram-2/). That is going to one hot a73, lthough it does have a optional active cooler, similar to how I set up my N2 with...
Forum: Mlucas 2020-07-22, 11:07
Replies: 116
Views: 8,249
Posted By paulunderwood
I only use the a73. The a53 is idle. It is best...

I only use the a73. The a53 is idle. It is best to have two processes for 2 processors. I might fire up a double check for the a53. Running wavefront on it is too slow!
Showing results 1 to 25 of 1000

 
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