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Forum: Miscellaneous Math 2021-06-20, 05:04
Replies: 12
Views: 1,084
Posted By paulunderwood
Thumbs up Efficent Test

The efficient test is:


{
tst(n,r)=local(t=lift(Mod(1/2,n)^r));
gcd(t^2-1,n)==1&&
gcd(t-2,n)==1&&
kronecker(t-4,n)==-1&&
Mod(2,n)^(n-1)==1&&...
Forum: Miscellaneous Math 2021-06-20, 00:22
Replies: 12
Views: 1,084
Posted By paulunderwood
Cool Extra gcd

This test looks good:


{
tst(n,r)=local(t=lift(Mod(2,n)^r));
gcd(t^2-1,n)==1&&
gcd(2*t-1,n)==1&&
kronecker(1-4*t,n)==-1&&
Mod(2,n)^(n-1)==1&&...
Forum: Miscellaneous Math 2021-06-19, 08:02
Replies: 12
Views: 1,084
Posted By paulunderwood
Restricted domain variation

Here I test over

x^2-x+2^r where kronecker(1-4*2^r,n)==-1
x^2-x-2^r where kronecker(1+4*2^r,n)==-1

If r is even this is the same as:

2^(n-1)==1 (mod n)
x^((n+1)/2)==1 (mod n,...
Forum: Hardware 2021-06-13, 23:09
Replies: 195
Views: 26,566
Posted By paulunderwood
1. Check NUMA is on in BIOS whatever that is!...

1. Check NUMA is on in BIOS whatever that is! :smile:

2,
Installation:
sudo yum install numactl

To see the memory map:
numactl -H
To run yr_prog entirely binded to MCDRAM:
numactl -m 1...
Forum: Hardware 2021-06-13, 22:35
Replies: 195
Views: 26,566
Posted By paulunderwood
This is way out of my depth, but do you have a...

This is way out of my depth, but do you have a good reason for not using numactl in flat-mode? Have you tried timings using it?
Forum: sweety439 2021-06-13, 21:21
Replies: 11
Views: 172
Posted By paulunderwood
You have Windoze Install on it Sun's free...

You have Windoze
Install on it Sun's free Virtual Box
In Virtual Box install Ubuntu
In Ubuntu install the latest multi-core Primo
Profit

That old mono-processor software will not get you...
Forum: Hardware 2021-06-13, 03:11
Replies: 195
Views: 26,566
Posted By paulunderwood
1, is bad news. The access to the DIMMs must be...

1, is bad news. The access to the DIMMs must be much slower than the MCDRAM -- an expensive lesson. With them, do you have a great 68-instances P-1 machine? See the table on this page...
Forum: Miscellaneous Math 2021-06-11, 23:15
Replies: 12
Views: 1,084
Posted By paulunderwood
[n,P,Q,R]=[1162349, 2335, 1, 2234] fools tst4(). ...

[n,P,Q,R]=[1162349, 2335, 1, 2234] fools tst4().

I have now revised the test; I insist that gcd(Q^2-1,n)==1 and gcd(R^2-1,n)==1 as well. :grin:

...
Forum: Lounge 2021-06-11, 09:41
Replies: 396
Views: 56,457
Posted By paulunderwood
Like a fool I answered my phone. "This is your...

Like a fool I answered my phone. "This is your service provider, your router has been hacked and I am here to fix it", said the woman with an Indian accent. Step-by-step instructions to install...
Forum: Hardware 2021-06-10, 23:09
Replies: 195
Views: 26,566
Posted By paulunderwood
I run Debian Buster on my Phi. Forget...

I run Debian Buster on my Phi. Forget multithreading on these beasts. 64 instances is king for mine, although I am running 4 Primo instances with its 256 threads. I don't know how Ernst's code copes.
Forum: Miscellaneous Math 2021-06-10, 20:57
Replies: 12
Views: 1,084
Posted By paulunderwood
Well that was a lot of BS maths. I...

Well that was a lot of BS maths.



I have tested (with strong kroneckers and gcd(P,n)==1 and gcd(Q^2-R^2,n)==1) for Q=1 up to n < 10^6 and for all Q for n up to 1.8*10^4 with Pari/GP. When I get...
Forum: Miscellaneous Math 2021-06-09, 18:39
Replies: 145
Views: 8,335
Posted By paulunderwood
:dnftt:

:dnftt:
Forum: Miscellaneous Math 2021-06-08, 00:13
Replies: 12
Views: 1,084
Posted By paulunderwood
What is wrong with this argument? Let: ...

What is wrong with this argument?

Let:
x^2-P*x+Q=0
y^2-P*y-Q=0
s^2-P*s+R=0
t^2-P*t-R=0

Then:
x^2+y^2-P*(x+y)=0
Forum: Miscellaneous Math 2021-06-07, 07:35
Replies: 12
Views: 1,084
Posted By paulunderwood
tst4(9809, 577, 27, 171) fails, but if I add the...

tst4(9809, 577, 27, 171) fails, but if I add the remedy gcd(P,n)==1 all is good.
Forum: Miscellaneous Math 2021-06-06, 10:53
Replies: 12
Views: 1,084
Posted By paulunderwood
I have not yet found a counterexample to the...

I have not yet found a counterexample to the previous test.

I now propose a more general test:

{
tst(n,P,Q_i,Q_j)=
kronecker(P^2-4*Q_i)==-1&&
kronecker(P^2+4*Q_i)==-1&&...
Forum: And now for something completely different 2021-06-05, 14:18
Replies: 71
Views: 21,451
Posted By paulunderwood
These are not "top20" special forms at the...

These are not "top20" special forms at the PrimePages. They would take you 16 times as long each as the 10k digit primes you certified.
Forum: Miscellaneous Math 2021-06-02, 07:23
Replies: 10
Views: 347
Posted By paulunderwood
More attacks on our hard efforts! "Only 28709...

More attacks on our hard efforts! "Only 28709 digits" -- have you tried running Primo, even at 10k digits? it is O(log(n)^(4+eps)). It is not trivial to do such certifications. It is absurd to say...
Forum: Hardware 2021-06-01, 20:58
Replies: 195
Views: 26,566
Posted By paulunderwood
3*2^6000000-1 with 64 instances (optimal) is 4.15...

3*2^6000000-1 with 64 instances (optimal) is 4.15 ms/iter. About 7 hours per test. (Xeon Phi 7210) YMMV.
Forum: Operation Billion Digits 2021-05-30, 14:10
Replies: 11
Views: 1,113
Posted By paulunderwood
:crank: How do you propose to do PRP/LL...

:crank:

How do you propose to do PRP/LL tests? What hardware and on it how long do you expect a single test to complete?
Forum: Miscellaneous Math 2021-05-29, 05:31
Replies: 10
Views: 347
Posted By paulunderwood
These numbers take months if not years of...

These numbers take months if not years of certification on dedicated hardware. Maybe you could invest some time and money in the endeavors to provide such proofs instead of squawking about how...
Forum: And now for something completely different 2021-05-28, 17:24
Replies: 71
Views: 21,451
Posted By paulunderwood
Maybe you meant "PRP" :smile:

Maybe you meant "PRP" :smile:
Forum: And now for something completely different 2021-05-28, 16:09
Replies: 71
Views: 21,451
Posted By paulunderwood
The first two should be "prime", according to...

The first two should be "prime", according to Norman. Maybe the certificates are not easily available.
Forum: And now for something completely different 2021-05-26, 02:32
Replies: 63
Views: 4,518
Posted By paulunderwood
R8177207 is an official top PRP...

R8177207 is an official top PRP (http://www.primenumbers.net/prptop/prptop.php?page=1).

Currenlty it does not appear on PrimePages's repunit page (https://primes.utm.edu/top20/page.php?id=57).
Forum: Miscellaneous Math 2021-05-25, 05:47
Replies: 12
Views: 1,084
Posted By paulunderwood
New quest

With my observations about GCDs, I now have a new quest to fool:

tstab(n,a,b)=tst(n,a)&&tst(n,b)&&gcd(a^2-b^2,n)==1;
Forum: Miscellaneous Math 2021-05-23, 20:18
Replies: 10
Views: 261
Posted By paulunderwood
See my edit above.

See my edit above.
Showing results 1 to 25 of 1000

 
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