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Search: Posts Made By: paulunderwood
Forum: Math 2021-11-26, 23:49
Replies: 6
Views: 73
Posted By paulunderwood
More on the seed 3/2 for Wagstaff numbers. ...

More on the seed 3/2 for Wagstaff numbers.

Mod(Mod(x,W),x^2-3/2*x+1) is at the heart because S = S0 = 3/2 = x+1/x which leads to the recurrence S=S^2-2 mod W

The solution for x is ( 3/2 +-...
Forum: Math 2021-11-26, 22:38
Replies: 6
Views: 73
Posted By paulunderwood
I just found this works for (2/3)^-1 ...

I just found this works for (2/3)^-1

wag(q)=W=(2^q+1)/3;S0=S=Mod(3/2,W);for(i=2,q,S=S^2-2);S==S0;

So maybe there is some relationship between inverse seeds for Mersenne and Wagstaff. I.e if S0...
Forum: Miscellaneous Math 2021-11-26, 21:22
Replies: 64
Views: 20,372
Posted By paulunderwood
I don't know about what you are driving at, but...

I don't know about what you are driving at, but isn't a bit like "Goldbach" -- strong numerical evidence but no proof?

Anyway here is an interesting youtube video on prime gaps which sounds...
Forum: Number Theory Discussion Group 2021-11-26, 19:47
Replies: 30
Views: 5,525
Posted By paulunderwood
I have done the program with a while loop rather...

I have done the program with a while loop rather than a do-while loop. You can strip out the shifted functionality as it makes no difference to timings -- for a random number it does make sense but...
Forum: Wagstaff PRP Search 2021-11-26, 15:13
Replies: 6
Views: 285
Posted By paulunderwood
4*S = (2^q+4)/3 == 1 mod W. So S = 1/4 mod W...

4*S = (2^q+4)/3 == 1 mod W.

So S = 1/4 mod W

Therefore
S0 = 1/4
S1 = (1/4)^2 - 2 = -31/16
S2 = (-31/16)^2 - 2 = 449/256
....
S_{q-1} = X/4^2^(q-1). This will be X if W is 4-PRP -- aren't...
Forum: Wagstaff PRP Search 2021-11-26, 05:21
Replies: 6
Views: 285
Posted By paulunderwood
This looks promising. Prove it, if you can. ...

This looks promising. Prove it, if you can.

You might write the code as:


wag(q)=W=(2^q+1)/3;S0=S=Mod((2^(q-2)+1)/3,W);for(i=2,q,S=S^2-2);S==S0;
Forum: Number Theory Discussion Group 2021-11-26, 05:05
Replies: 30
Views: 5,525
Posted By paulunderwood
Quoting the excellent GMP website documentation: ...

Quoting the excellent GMP website documentation:



I changed "fdiv" to "cdiv" and all is well with Bernhard's problematic example. :grin:

Bernhard should think of these artifacts as a...
Forum: Linux 2021-11-21, 17:04
Replies: 6
Views: 578
Posted By paulunderwood
That's a nice graphical way of doing it, but I am...

That's a nice graphical way of doing it, but I am unsure that before copying the OS you can select /dev/sdaX. I don't want the other partitions to be destroyed. It seems to be, after a firmware...
Forum: Probability & Probabilistic Number Theory 2021-11-20, 14:01
Replies: 13
Views: 1,217
Posted By paulunderwood
The row of data for 9 digits has been added. The...

The row of data for 9 digits has been added. The data for 10 digits will take another month of so.

I have tried to make the English simpler. So it is worth downloading the latest copy from post #1...
Forum: Miscellaneous Math 2021-11-16, 23:54
Replies: 0
Views: 46
Posted By paulunderwood
1+1 selfridges test for 1/8 of numbers

I was playing around while I waiting for some results to come in...

For n=3 mod 4 such that kronecker(-3,n)==-1 and kronecker(-7,n)==-1 test

Mod(2,n)^((n-1)/2)==kronecker(2,n) and...
Forum: Riesel Prime Search 2021-11-16, 18:04
Replies: 98
Views: 27,388
Posted By paulunderwood
It is not available for armhf64. Our only hope is...

It is not available for armhf64. Our only hope is that somehow Ernst's Mlucas library could do it. Ernst? Pi's etc are much slower than AMD/Intel x86/x64 at crunching mega bit numbers
Forum: Miscellaneous Math 2021-11-16, 17:33
Replies: 5
Views: 667
Posted By paulunderwood
There is nothing "fast" about it. Primo is just...

There is nothing "fast" about it. Primo is just as fast. Of course it would be nice to have a 128 core ECPP program, if not more cores!

Maybe the Pari-MPI team will make their ECPP software...
Forum: And now for something completely different 2021-11-14, 00:06
Replies: 55
Views: 9,138
Posted By paulunderwood
The same reasoning why a CPAP-11 has yet to be...

The same reasoning why a CPAP-11 has yet to be found: https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression#Consecutive_primes_in_arithmetic_progression

I found precomputing the primorial...
Forum: And now for something completely different 2021-11-13, 23:23
Replies: 55
Views: 9,138
Posted By paulunderwood
Very nice! Did you use a lot of cycles sieving...

Very nice! Did you use a lot of cycles sieving and PRP'ing?
Forum: Number Theory Discussion Group 2021-11-13, 22:47
Replies: 30
Views: 5,525
Posted By paulunderwood
In that case you need: void mpz_mod_mp...

In that case you need:

void mpz_mod_mp (mpz_t r, mpz_t A, mp_bitcnt_t p)
{
mpz_t a;
mpz_init_set(a, A);
do
{
mpz_fdiv_r_2exp(r, a, p);
mpz_fdiv_q_2exp(a, a,...
Forum: Number Theory Discussion Group 2021-11-13, 21:50
Replies: 30
Views: 5,525
Posted By paulunderwood
Here is my solution written in C #include...

Here is my solution written in C

#include <gmp.h>
#include <stdio.h>
#include <stdlib.h>

void mpz_mod_mp (mpz_t r, mpz_t a, mp_bitcnt_t p)
{
// assumed that r is initialized and a is...
Forum: Number Theory Discussion Group 2021-11-13, 20:18
Replies: 30
Views: 5,525
Posted By paulunderwood
Has it been initialized?

Has it been initialized?
Forum: Number Theory Discussion Group 2021-11-13, 20:08
Replies: 30
Views: 5,525
Posted By paulunderwood
can you output p and f in that function for us to...

can you output p and f in that function for us to see?
Forum: Number Theory Discussion Group 2021-11-13, 19:51
Replies: 30
Views: 5,525
Posted By paulunderwood
Without checking the manual that may well be the...

Without checking the manual that may well be the case, but mpz_sizeinbase returns an int?
Forum: Number Theory Discussion Group 2021-11-13, 19:24
Replies: 30
Views: 5,525
Posted By paulunderwood
It usual for p to be a prime and Mp to be the...

It usual for p to be a prime and Mp to be the corresponding Mersenne number. If you have passed in p then why do you need Mp?

What is f?
Forum: MattcAnderson 2021-11-12, 11:08
Replies: 11
Views: 285
Posted By paulunderwood
In your opinion. Or can you prove the prime...

In your opinion. Or can you prove the prime numbers are platonic (https://en.wikipedia.org/wiki/Theory_of_forms)?
Forum: MattcAnderson 2021-11-12, 10:09
Replies: 11
Views: 285
Posted By paulunderwood
Would you "opinion" still exist when "the closest...

Would you "opinion" still exist when "the closest stars burn out and become dark"? Ergo would "1+1=2"?
Forum: CADO-NFS 2021-11-11, 21:20
Replies: 18
Views: 764
Posted By paulunderwood
What are the symptoms? Sometimes all it takes is...

What are the symptoms? Sometimes all it takes is a new CR 2032 battery for the mainboard. :smile:
Forum: Linux 2021-11-11, 06:36
Replies: 6
Views: 578
Posted By paulunderwood
Another method is to install to an SD card and...

Another method is to install to an SD card and rsync its already formatted partitions to the USB partitions. Then make a few changes to /etc/fstab on the USB copy.. Run grub-install on a file which...
Forum: Flea Market 2021-11-10, 22:37
Replies: 26
Views: 1,222
Posted By paulunderwood
I guess Intel has been blasting the airwaves with...

I guess Intel has been blasting the airwaves with their 8080-based wares :wink:
Showing results 1 to 25 of 1000

 
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