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Forum: And now for something completely different 2020-09-30, 18:21
Replies: 1
Views: 47
Posted By paulunderwood
Pari uses two functions: isprime() and...

Pari uses two functions: isprime() and ispseudoprime(). They are about the same for n<2^64. The latter is a probablistic test that since its conception in the '80's has no known counterexample -- I...
Forum: Miscellaneous Math 2020-09-28, 17:04
Replies: 104
Views: 8,647
Posted By paulunderwood
Question x^2-y test

I have devised another PRP for odd non-square n:

Let y = 2^r-1

Then seek

gcd(r-1,n-1)==1
kronecker(y,n)==-1

and test
Forum: Miscellaneous Math 2020-09-28, 15:26
Replies: 6
Views: 89
Posted By paulunderwood
Re-writing your terrible use of brackets... ...

Re-writing your terrible use of brackets...

2^(p-2)- 7 - ((a*(a+1)/2) - 1)*6 has the same symbol over M_p as:

2^(p-2) - 1 - 3*a*(a+1) same as

2^p -4 - 12*a*(a+1) same as

-3 - 12*a*(a+1)...
Forum: Miscellaneous Math 2020-09-28, 14:40
Replies: 6
Views: 89
Posted By paulunderwood
2^(p-2)-7 has the same residue as 2^p - 7*4; same...

2^(p-2)-7 has the same residue as 2^p - 7*4; same as 1 -7*4; same as -27; same as -3, and this is always true for odd Mersenne. LL is the same as x^(n+1)==1 mod (M_p, x^2-4*x+1) and the polynomial...
Forum: Miscellaneous Math 2020-09-28, 14:23
Replies: 6
Views: 89
Posted By paulunderwood
It is true for all odd prime p that...

It is true for all odd prime p that kronecker(2^(p-2)-7,2^p-1) == 1. What is your point?
Forum: GpuOwl 2020-09-28, 11:04
Replies: 62
Views: 2,188
Posted By paulunderwood
Maybe there were too many GCD happening at once...

Maybe there were too many GCD happening at once on your multi card system. See this post (https://mersenneforum.org/showpost.php?p=547643&postcount=1) on how to limit the RAM requirements for...
Forum: Data 2020-09-28, 08:49
Replies: 527
Views: 49,558
Posted By paulunderwood
4132590s (47.8 days)...

4132590s (47.8 days) (https://mersenneforum.org/showpost.php?p=557830&postcount=17) on Gelly's 32 core AMD Threadripper
Forum: Data 2020-09-28, 04:04
Replies: 527
Views: 49,558
Posted By paulunderwood
Gelly has proved the M84,211 cofactor...

Gelly has proved the M84,211 cofactor (https://primes.utm.edu/primes/page.php?id=131278). The page https://www.mersenne.ca/prp.php needs to be updated.
Forum: And now for something completely different 2020-09-28, 03:57
Replies: 18
Views: 4,442
Posted By paulunderwood
It is up...

It is up (https://primes.utm.edu/primes/page.php?id=131278).
Forum: Miscellaneous Math 2020-09-28, 03:49
Replies: 104
Views: 8,647
Posted By paulunderwood
It is good up to 10^13 the verification of which...

It is good up to 10^13 the verification of which took about 5 days on 1 core with GMP. If znorder is large for a particular n then it takes that n a few hours. I am going to put verification on the...
Forum: And now for something completely different 2020-09-25, 12:49
Replies: 18
Views: 4,442
Posted By paulunderwood
:banana: Congrats for the proof of the M84211...

:banana: Congrats for the proof of the M84211 cofactor.
Forum: Programming 2020-09-24, 00:30
Replies: 15
Views: 2,357
Posted By paulunderwood
I don't think GMP switch to special k*b^n+-c like...

I don't think GMP switch to special k*b^n+-c like PFGW's implementation of GWNUM.

Also PFGW uses GMP below a certain threshold.

If GMP has improved PRP times then maybe the author, "rogue",...
Forum: Lounge 2020-09-24, 00:14
Replies: 12
Views: 535
Posted By paulunderwood
LLR or PRP? Ben trial divides to the square root,...

LLR or PRP? Ben trial divides to the square root, because he can!
Forum: Miscellaneous Math 2020-09-23, 23:41
Replies: 104
Views: 8,647
Posted By paulunderwood
It is ad hoc. b=3 and all powers of 3 give...

It is ad hoc. b=3 and all powers of 3 give counterexamples. I have not found any for b=5 -- I can't recall b=7 counterexample.

By plugging in primes to the aforementioned program will show you...
Forum: Miscellaneous Math 2020-09-23, 23:16
Replies: 104
Views: 8,647
Posted By paulunderwood
b=2, b=4 and b=8 seems to give counterexamples 7...

b=2, b=4 and b=8 seems to give counterexamples 7 mod 8, as you can see by running the Pari/GP program given in that post.
Forum: Miscellaneous Math 2020-09-23, 22:50
Replies: 104
Views: 8,647
Posted By paulunderwood
Thumbs up Paper + Program

Here is a "flawless" replacement paper to a previous paper (https://mersenneforum.org/showthread.php?t=24051&page=8). :book:

I have also attached the GMP program used to log cases where GCDs were...
Forum: Miscellaneous Math 2020-09-23, 22:20
Replies: 104
Views: 8,647
Posted By paulunderwood
Thumbs down This thread is supposed to be about PRP tests...

This thread is supposed to be about PRP tests using bases over restricted domains, as the content (up until now) shows. It is not really about base changes or coloured balls! Please keep your tripe...
Forum: Miscellaneous Math 2020-09-22, 17:02
Replies: 104
Views: 8,647
Posted By paulunderwood
Cool I can tighten things up by doing the following...

I can tighten things up by doing the following test (for any a=2^r):


gcd(a-2,n)==1
gcd(a-4,n)==1
kronecker(1-a,n)==-1
Mod(1-a,n)^((n-1)/2)==-1
Mod(2,n)^((n-1)/2)==kronecker(2,n)
...
Forum: GPU Computing 2020-09-22, 10:02
Replies: 10
Views: 378
Posted By paulunderwood
Here are parts of my /etc/default/grub ...

Here are parts of my /etc/default/grub
GRUB_CMDLINE_LINUX_DEFAULT="quiet amdgpu.ppfeaturemask=0xffffffff"
and /boot/grub/grub.cfg
linux /boot/vmlinuz-4.19.0-10-amd64...
Forum: GPU Computing 2020-09-22, 07:24
Replies: 10
Views: 378
Posted By paulunderwood
I ran apt-get update (Debian) and the system...

I ran apt-get update (Debian) and the system froze while installing ROCm-3.8.0 with the message "building initial module for 4.19-0-9-amd64". Rebooted. I had to do dpkg --configure -a (??) and it...
Forum: GPU Computing 2020-09-22, 04:50
Replies: 10
Views: 378
Posted By paulunderwood
Are you using Linux or Windows? Has the OS...

Are you using Linux or Windows? Has the OS upgraded recently?
Forum: Miscellaneous Math 2020-09-19, 17:44
Replies: 104
Views: 8,647
Posted By paulunderwood
Cool A variation on the theme

I have been considering x^2-2*x+2^r=0 and have been taking n+1 powers of x over it. I can also take n+1 powers over x^2-(4/2^r-2)+1 and expect the answer to be 1. This gives rise to (yet) another...
Forum: Miscellaneous Math 2020-09-19, 09:04
Replies: 104
Views: 8,647
Posted By paulunderwood
Letting r=1 is trivial as the Euler part becomes...

Letting r=1 is trivial as the Euler part becomes Mod(-1)^((n-1)/2). Also it is specified gcd(2-2^r,n)==1 because of x^2-(2^2/2^r-2)*x+1

r=2 does not pass gcd(4-2^r,n)==1. This comes from...
Forum: GpuOwl 2020-09-18, 09:56
Replies: 56
Views: 4,786
Posted By paulunderwood
I think you should have decreased it.

I think you should have decreased it.
Forum: Miscellaneous Math 2020-09-17, 16:41
Replies: 104
Views: 8,647
Posted By paulunderwood
Your idea seems right. I ran some of this: {...

Your idea seems right. I ran some of this:

{
forstep(n=30169231,30169231,2,
if(!ispseudoprime(n)&&!issquare(n),
for(b=1,n,if(gcd(b,n)==1,z=znorder(Mod(b,n));
for(r=1,z,A=Mod(b,n)^r;...
Showing results 1 to 25 of 1000

 
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