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Search: Posts Made By: paulunderwood
Forum: Miscellaneous Math 2022-11-27, 01:04
Replies: 20
Views: 1,230
Posted By paulunderwood
Hah, I made a complete blunder. The conclusion is...

Hah, I made a complete blunder. The conclusion is 1=1. I have marked it with a red X.
Forum: Miscellaneous Math 2022-11-26, 17:05
Replies: 20
Views: 1,230
Posted By paulunderwood
Partial proof

For a basis we know prime \(p\) that \(x^{p+1} \equiv -3 \pmod{n, x^2-3^rx-3}\) where the Jacobi symbol of the discriminant is \(-1\).

Now suppose \(n=pq\) where \(q>1\) not necessarily prime.
...
Forum: Miscellaneous Math 2022-11-26, 10:17
Replies: 20
Views: 1,230
Posted By paulunderwood
partial results

The GCD-less test for "-12" was verrified using Par/GP my forumite mart_t and me up to 1.2*10^12.

The test for "-3" has now reached 10^12 using GMP+primesieve. It will take a couple of Celeron CPU...
Forum: And now for something completely different 2022-11-25, 20:45
Replies: 207
Views: 22,569
Posted By paulunderwood
Looking at the source for lib/nt.c I see: ...

Looking at the source for lib/nt.c I see:

unsigned long int cm_nt_next_prime (const unsigned long int n)
/* returns the prime following n */

{
static bool init = true;
#ifdef WITH_MPI...
Forum: And now for something completely different 2022-11-25, 05:06
Replies: 181
Views: 43,304
Posted By paulunderwood
Done: Certified and registered at The Prime Pages...

Done: Certified and registered at The Prime Pages (https://primes.utm.edu/primes/page.php?id=134576) and factorDB.

Reserving the M216317 cofactor (https://www.mersenne.ca/exponent/216317)...
Forum: Data 2022-11-25, 04:57
Replies: 592
Views: 129,505
Posted By paulunderwood
I have just made a submission to The Prime Pages...

I have just made a submission to The Prime Pages and uploaded the certificate do factorDB for the M174533 cofactor (https://primes.utm.edu/primes/page.php?id=134576). :flex:
Forum: And now for something completely different 2022-11-24, 00:42
Replies: 207
Views: 22,569
Posted By paulunderwood
I have had a dreaded "*** No suitable curve...

I have had a dreaded "*** No suitable curve found!" at about 20k digits of a 52k digit number. Re-running after reboot to see if it happens again. What can I do to remedy it?

Interestingly instead...
Forum: Lounge 2022-11-23, 17:12
Replies: 2,016
RIP
Views: 263,055
Posted By paulunderwood
Wilko Johnson

https://www.theguardian.com/music/2022/nov/23/wilko-johnson-obituary

A great punk era inspiring guitarist!

Yp2DvPKh118
Forum: mersenne.ca 2022-11-23, 14:09
Replies: 973
Sticky: mersenne.ca
Views: 137,757
Posted By paulunderwood
Thanks for testing. Rebooting my router seems to...

Thanks for testing. Rebooting my router seems to hve fixed the issue. :tu:
Forum: mersenne.ca 2022-11-23, 14:00
Replies: 973
Sticky: mersenne.ca
Views: 137,757
Posted By paulunderwood
504

I am getting 504 Gateway Time-out on https://www.mersenne.ca/prp.php :down:
Forum: And now for something completely different 2022-11-22, 02:39
Replies: 207
Views: 22,569
Posted By paulunderwood
It should be #include <gmp.h> and not #include...

It should be #include <gmp.h> and not #include "gmp.h". Does this change fix your problem?
Forum: And now for something completely different 2022-11-21, 22:35
Replies: 207
Views: 22,569
Posted By paulunderwood
For GMP have you either installed libgmp-dev...

For GMP have you either installed libgmp-dev (debian based systems) or ./configure && make && make check && sudo make install in the GMP directory? With either of these ways compiling with #include...
Forum: PrimeNet 2022-11-21, 19:27
Replies: 24
Views: 947
Posted By paulunderwood
Do the math: core count times GHz, and compare. ...

Do the math: core count times GHz, and compare.
"
I think lower "time" is better.
Forum: PrimeNet 2022-11-21, 19:19
Replies: 24
Views: 947
Posted By paulunderwood
Could this laptop of yours be TDP limited? That...

Could this laptop of yours be TDP limited? That might be what's happening.
Forum: Information & Answers 2022-11-21, 18:37
Replies: 1
Views: 277
Posted By paulunderwood
Your computer has had 1 Gerbicz EDAC (Error...

Your computer has had 1 Gerbicz EDAC (Error detection and correction), Things are rosy.

Install some temperature measuring software. Things to watch out for are:


temperature
voltage
...
Forum: Miscellaneous Math 2022-11-21, 06:51
Replies: 20
Views: 1,230
Posted By paulunderwood
I fixed a few things in the paper that were...

I fixed a few things in the paper that were mistakes.

A GMP+primesieve program is now running here. It is much faster tha the Pari/GP one.

I posted on Math.StackExchange but the thread was...
Forum: Miscellaneous Math 2022-11-20, 05:34
Replies: 20
Views: 1,230
Posted By paulunderwood
Here is a short paper about this Lucas(n,3^r,-3)...

Here is a short paper about this Lucas(n,3^r,-3) test.

Now I have to get into coding up a verification program written with GMP+primesieve. Pari/GP is too slow for the purpose.

As I say in the...
Forum: Lounge 2022-11-19, 22:22
Replies: 33
Views: 856
Posted By paulunderwood
Despite what FIFA have said about human rights in...

Despite what FIFA have said about human rights in The West over the last 3 millennia, Qatar's record on anything that is not totally male dominance and workers' safety is atrocious. I guess bribery...
Forum: Miscellaneous Math 2022-11-15, 07:30
Replies: 20
Views: 1,230
Posted By paulunderwood
(Lucas) Q=-3 seems the natural base to study as...

(Lucas) Q=-3 seems the natural base to study as it is the discriminant of z^2+-z+1.

In practice, avoidance of z^2-z+1 seems sufficient. This divides z^3+1 which divides z^6-1.

We have...
Forum: Miscellaneous Math 2022-11-14, 11:47
Replies: 20
Views: 1,230
Posted By paulunderwood
A proof?

We are busy verifying to 10^12, the test for the test over x^2-12^r*x-12 where x^(n+1)==-12.

I notice that the discriminant is 1+48 == 49 for r=0, i.e a square.

Anyway back to the "proof" and...
Forum: Software 2022-11-11, 23:19
Replies: 12
Views: 1,038
Posted By paulunderwood
Fortunately, despite 15 years of growth it has...

Fortunately, despite 15 years of growth it has not inside my mouth. Otherwise they would have to extract a tooth and saw trough my jaw in order to remove the tumour. I am looking forward to recovery.
Forum: Miscellaneous Math 2022-11-11, 09:37
Replies: 20
Views: 1,230
Posted By paulunderwood
The pattern broke for +12, with n=20935371731 and...

The pattern broke for +12, with n=20935371731 and r=6163, yet gcd(2*r-1,n-1)==145.

Testing of -12 is going great guns. Now at n>32,000,000,000, with no output except way points.
Forum: Miscellaneous Math 2022-11-11, 02:12
Replies: 20
Views: 1,230
Posted By paulunderwood
As well as "-12" I am running "+12" overnight....

As well as "-12" I am running "+12" overnight. The latter has the following pattern so far:


g := g(2*r-1,n-1).
one solution for r up to z the multiplicative order of 12 mod n
g = z
n%4 =...
Forum: Software 2022-11-10, 23:58
Replies: 12
Views: 1,038
Posted By paulunderwood
We are so glad your heart operation and Mac...

We are so glad your heart operation and Mac operation went well, Ernst. :tu:

I am under the knife on Wednesday to have a second operation on the other side of my face to have a bilateral Warthin...
Forum: Miscellaneous Math 2022-11-10, 23:41
Replies: 20
Views: 1,230
Posted By paulunderwood
In the "wood" it looks like I found a clearing...

In the "wood" it looks like I found a clearing where there is no tree!

I could speed up testing by letting a=lift(Mod(-12,n)^r) and pretesting with kronecker(a^2+48,n)==-1 :ermm:

:xmastree:
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