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Forum: Hardware 2021-06-13, 03:11
Replies: 186
Views: 25,867
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: 9
Views: 868
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: 56,146
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: 186
Views: 25,867
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: 9
Views: 868
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: 128
Views: 6,674
Posted By paulunderwood
:dnftt:

:dnftt:
Forum: Miscellaneous Math 2021-06-08, 00:13
Replies: 9
Views: 868
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: 9
Views: 868
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: 9
Views: 868
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: 70
Views: 20,771
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: 268
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: 186
Views: 25,867
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: 792
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: 268
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: 70
Views: 20,771
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: 70
Views: 20,771
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: 4,301
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: 9
Views: 868
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: 245
Posted By paulunderwood
See my edit above.

See my edit above.
Forum: Miscellaneous Math 2021-05-23, 20:03
Replies: 10
Views: 245
Posted By paulunderwood
We have (2^a-1)*(2^b-1) = 2^(a+b)-(2^a+2^b)+1. So...

We have (2^a-1)*(2^b-1) = 2^(a+b)-(2^a+2^b)+1. So there is a simple pattern to be found. I leave it to you to find and implement it. :smile:

Just worked it out: assume a> b. Then it is (b-1) 1's,...
Forum: Miscellaneous Math 2021-05-23, 13:47
Replies: 10
Views: 245
Posted By paulunderwood
So in binary it is (n-1) 1's followed by n 0's...

So in binary it is (n-1) 1's followed by n 0's and ends with 1. Is this what your code does?
Forum: Miscellaneous Math 2021-05-23, 13:35
Replies: 9
Views: 868
Posted By paulunderwood
fooled

tst(10627*148793, 479362525) fools!
Forum: Miscellaneous Math 2021-05-23, 13:22
Replies: 10
Views: 245
Posted By paulunderwood
Does it use the identity Mp^2 = (Mp+1)^2-2*Mp-1?

Does it use the identity Mp^2 = (Mp+1)^2-2*Mp-1?
Forum: Miscellaneous Math 2021-05-21, 14:16
Replies: 9
Views: 868
Posted By paulunderwood
Let's turn the above into Pari/GP code: {...

Let's turn the above into Pari/GP code:


{
tst(n,a)=
kronecker(a^2-4*a,n)==-1&&
kronecker(a^2+4*a,n)==-1&&
Mod(a,n)^((n-1)/2)==kronecker(a,n)&&...
Forum: Lounge 2021-05-18, 16:05
Replies: 250
Views: 39,531
Posted By paulunderwood
Not true. it will be 15 0's followed by 9. ...

Not true. it will be 15 0's followed by 9.

:orly owl:
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