mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 1000
Search took 0.27 seconds.
Search: Posts Made By: paulunderwood
Forum: And now for something completely different 2021-04-21, 15:28
Replies: 22
Views: 674
Posted By paulunderwood
I am currently testing it for Lucas over x^2-4*x+1

I am currently testing it for Lucas over x^2-4*x+1
Forum: Riesel Prime Search 2021-04-20, 22:08
Replies: 243
Views: 41,056
Posted By paulunderwood
The rep-digit is an admirable find.

The rep-digit is an admirable find.
Forum: And now for something completely different 2021-04-20, 22:07
Replies: 22
Views: 674
Posted By paulunderwood
That is one hell of a PRP. Congrats on such a...

That is one hell of a PRP. Congrats on such a large find. :smile:
Forum: Factoring 2021-04-20, 17:42
Replies: 32
Views: 856
Posted By paulunderwood
You will probably have to install the ssh server...

You will probably have to install the ssh server with sudo apt-get install openssh-server.

Debian shuts down after 20 mins after a fresh install and it is necessary to mask power saving. See this...
Forum: Miscellaneous Math 2021-04-19, 20:26
Replies: 26
Views: 549
Posted By paulunderwood
You have described the LL test and a Fermat base...

You have described the LL test and a Fermat base 3 PRP test.

There are many tricks to speed up computation for Mersenne numbers. :smile:
Forum: Homework Help 2021-04-19, 11:36
Replies: 9
Views: 188
Posted By paulunderwood
https://en.wikipedia.org/wiki/Principia_Mathematic...

https://en.wikipedia.org/wiki/Principia_Mathematica

A very soporific read!
Forum: Homework Help 2021-04-18, 14:14
Replies: 9
Views: 188
Posted By paulunderwood
(a+b)^2 means A*B where A=B=a+b ...

(a+b)^2 means A*B where A=B=a+b
(a+b)*(a+b)=a*(a+b)+b*(a+b) with right distribution
a*(a+b)+b*(a+b)=a^2+a*b+b*a+b^2 with two applications of left distribution
The desired result follows...
Forum: Homework Help 2021-04-18, 13:15
Replies: 9
Views: 188
Posted By paulunderwood
You'll have to use the distributive laws (and...

You'll have to use the distributive laws (and rearrange terms using the axiom you mentioned). :smile:
Forum: Miscellaneous Math 2021-04-15, 11:39
Replies: 13
Views: 302
Posted By paulunderwood
No matter how many -- a reasonable number -- MR...

No matter how many -- a reasonable number -- MR tests you do there will be counterexamples. 1+1..+1+1 selfridges is a poor test and cryptographically weak. This is one of the reasons why GMP now...
Forum: Miscellaneous Math 2021-04-09, 19:21
Replies: 35
Views: 690
Posted By paulunderwood
Whatever you do with 1+1+1+..+1+2 selfridges...

Whatever you do with 1+1+1+..+1+2 selfridges there will always be counterexamples if you allow a free parameter. I am not saying there will not exist counterexamples for 1+1+1..+1+2+2 -- they are...
Forum: Miscellaneous Math 2021-04-09, 00:41
Replies: 35
Views: 690
Posted By paulunderwood
Nice try. n==3 mod 4 has no counterexample for...

Nice try. n==3 mod 4 has no counterexample for the two selfridges test (2+i)^(n+1)==5 mod (n,i^2+1) for n<2^50.
Forum: Miscellaneous Math 2021-04-06, 14:35
Replies: 35
Views: 690
Posted By paulunderwood
Can you express your algorithm in Pari/GP for us?...

Can you express your algorithm in Pari/GP for us? Then it will be easier to understand and easier to test (to destruction).

If you are working over the complex numbers then raising the base a+b*i...
Forum: Miscellaneous Math 2021-04-03, 23:47
Replies: 35
Views: 690
Posted By paulunderwood
Please give us a worked example for the prime 97....

Please give us a worked example for the prime 97. :smile:
Forum: Tales From the Crypt(o) 2021-04-03, 21:55
Replies: 280
Views: 68,191
Posted By paulunderwood
Our beloved leader (in the UK) is going to...

Our beloved leader (in the UK) is going to propose "Covid Passports", a Chinese-like control of the population surreptitiously under the guise of "using every tool in the toolbox to restore the...
Forum: Factoring 2021-04-02, 20:31
Replies: 32
Views: 856
Posted By paulunderwood
I have been Windows-free for at least 20 years. I...

I have been Windows-free for at least 20 years. I started out on a ZX81; at Uni used PRIMOS and a DEC VAX system. For my sins I had to use DOS and completed rejected Windows during the 90's when it...
Forum: Factoring 2021-04-01, 19:45
Replies: 32
Views: 856
Posted By paulunderwood
All Linux here. You'll find Linux easier to...

All Linux here. You'll find Linux easier to configure to best suit your needs, Be free!
Forum: GPU Computing 2021-03-22, 14:10
Replies: 3
Views: 375
Posted By paulunderwood
Apart from Ubuntu, Fedora is a better choice than...

Apart from Ubuntu, Fedora is a better choice than Centos,
Forum: Miscellaneous Math 2021-03-18, 21:53
Replies: 118
Views: 24,240
Posted By paulunderwood
odd r

Let a=2^r, r odd and minimal such that kronecker(a^2-1,n)==-1
Test1. Mod(a^2-1.n)^((n-1)/2)==-1
Test2. Mod(Mod(2*x,n),x^2-2*a*a+1)^((n+1)/2)==2*kronecker(a+1)


Interestingly counterexamples...
Forum: Miscellaneous Math 2021-03-18, 19:41
Replies: 118
Views: 24,240
Posted By paulunderwood
If n = 2^s+-3, letting b = 5 would mean 2^s-2...

If n = 2^s+-3, letting b = 5 would mean 2^s-2 would okay for a base or 2^s -8 would also be okay for a base, since neither are powers ;
of 2. So apart from these corner cases taking b=3 should be...
Forum: Miscellaneous Math 2021-03-18, 06:24
Replies: 118
Views: 24,240
Posted By paulunderwood
Getting back on track for this thread... ...

Getting back on track for this thread...


Let b != +-2^s
Let a = b^r where kronecker(a^2-1,n) == -1
Test1: (a^2-1,n)^((n-1)/2) == -1 (mod n)
Test2: (b*x)^((n+1)/2) ==...
Forum: Miscellaneous Math 2021-03-17, 11:07
Replies: 58
Views: 1,411
Posted By paulunderwood
http://www.numbertheory.org/ntw/N6.html ...

http://www.numbertheory.org/ntw/N6.html

http://www.numbertheory.org/ntw/N7.html

Why do you not attach it here at MeresenneForum first? At least we can advise you on spelling and typographic...
Forum: Software 2021-03-15, 22:20
Replies: 13
Views: 412
Posted By paulunderwood
Hmm, two workers would do it. Then try four and...

Hmm, two workers would do it. Then try four and compare throughput.

I think mprime and the Linux scheduler are smart enough to set the right affinities.
Forum: Software 2021-03-15, 20:53
Replies: 13
Views: 412
Posted By paulunderwood
Try 2 instances of 26 cores each, one for each...

Try 2 instances of 26 cores each, one for each CPU. And then try 4 instances of 13 cores each and compare throughputs.
Forum: GPU Computing 2021-03-15, 20:39
Replies: 365
Views: 63,741
Posted By paulunderwood
You should be able to afford it if you find the...

You should be able to afford it if you find the next Mersenne prime :wink:
Forum: And now for something completely different 2021-03-15, 16:58
Replies: 48
Views: 17,084
Posted By paulunderwood
Talking Reserving: M86137 cofactor prp25896 M86371...

Reserving:

M86137 cofactor prp25896
M86371 cofactor prp25984
M87691 cofactor prp26371
E(11848)/(5*1582043) prp40792
Showing results 1 to 25 of 1000

 
All times are UTC. The time now is 12:09.

Thu Apr 22 12:09:03 UTC 2021 up 14 days, 6:49, 0 users, load averages: 2.13, 2.08, 1.99

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, 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.