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Forum: And now for something completely different 2020-09-25, 12:49
Replies: 17
Views: 4,213
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: 2,266
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: 518
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: 102
Views: 8,331
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: 102
Views: 8,331
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: 102
Views: 8,331
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: 102
Views: 8,331
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: 102
Views: 8,331
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: 341
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: 341
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: 341
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: 102
Views: 8,331
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: 102
Views: 8,331
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: 4,704
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: 102
Views: 8,331
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;...
Forum: GpuOwl 2020-09-17, 05:24
Replies: 2,485
Views: 147,336
Posted By paulunderwood
I can't help. I have never used colab.

I can't help. I have never used colab.
Forum: GpuOwl 2020-09-17, 05:18
Replies: 2,485
Views: 147,336
Posted By paulunderwood
This is not a bash terminal. Are you using...

This is not a bash terminal. Are you using "colab"?
Forum: GpuOwl 2020-09-17, 05:05
Replies: 2,485
Views: 147,336
Posted By paulunderwood
No no. At the terminal enter g++ --version ...

No no. At the terminal enter g++ --version

Also try g++ followed by hitting tab a couple of times.
Forum: GpuOwl 2020-09-17, 04:43
Replies: 2,485
Views: 147,336
Posted By paulunderwood
What does g++ --version say? You might have...

What does g++ --version say?

You might have to hardwire your compiler name and version in gpuOwl's makefile.
Forum: Miscellaneous Math 2020-09-16, 13:42
Replies: 54
Views: 1,605
Posted By paulunderwood
Once again it is meaningless to talk about...

Once again it is meaningless to talk about "u>log(p)^2" when working with modular arithmetic. Also it makes absolutely no difference where you apply modulo operations. It is a "multiplicative...
Forum: Miscellaneous Math 2020-09-15, 18:52
Replies: 102
Views: 8,331
Posted By paulunderwood
Efficiencies

Using Euler+Frobenius on x=1+-sqrt(1-b^4). For intermediate values s*x+t in left-right exponentiation of the Frobenius test we have:-

Squaring:
? Mod(s*x+t,x^2-2*x+b^4)^2
Mod((2*s^2 + 2*t*s)*x +...
Forum: Miscellaneous Math 2020-09-15, 15:50
Replies: 12
Views: 317
Posted By paulunderwood
Mod(10,107)^10000000000000000000000000000000000000...

Mod(10,107)^100000000000000000000000000000000000000000
Mod(34, 107)

##
*** last result computed in 0 ms.

It actually works by left-right binary exponentiation modulo n...
Forum: Miscellaneous Math 2020-09-15, 15:21
Replies: 12
Views: 317
Posted By paulunderwood
This Robert at his computer: :primenet: ...

This Robert at his computer:
:primenet:

Know that a*b mod n is the same as (a mod n) * (b mod n) :smile:
Forum: Miscellaneous Math 2020-09-15, 14:06
Replies: 102
Views: 8,331
Posted By paulunderwood
I made a mistake: Case 4 of FLT...

I made a mistake: Case 4 of FLT (https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Proofs_for_specific_exponents) uses the fact a^4-b^4 is never a square. So I have to flip the sign to get:

...
Forum: Miscellaneous Math 2020-09-15, 10:44
Replies: 102
Views: 8,331
Posted By paulunderwood
test based on FLT proof n=4

In the previous I had x=1+-sqrt(1-2^r). I note that 2^r-1 (r>1) is never a square. So what else is never a square? In his proof of FLT case n=4 Fermat showed a^4+b^4 is never a square, which leads me...
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