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Forum: And now for something completely different 2021-11-28, 22:16
Replies: 13
Views: 7,430
Posted By paulunderwood
Another way to do it with Pari-GP is...

Another way to do it with Pari-GP is 2^89\10^2%10^21 where the infix operator \ gives the quotient.
Forum: Miscellaneous Math 2021-11-28, 14:42
Replies: 429
Views: 39,820
Posted By paulunderwood
Sorry for the confusion. I was just referring to...

Sorry for the confusion. I was just referring to Tucker's blunder in general.
Forum: Miscellaneous Math 2021-11-28, 08:07
Replies: 429
Views: 39,820
Posted By paulunderwood
Gender populations are not 50::50. Most forumites...

Gender populations are not 50::50. Most forumites here happen to be male. Some people like to identify as non-binary gender. "Dobri" is mainly a man's name. Like your guess at 168Mb for the next...
Forum: And now for something completely different 2021-11-28, 07:50
Replies: 82
Views: 26,291
Posted By paulunderwood
Welcome back to the fold. I should be...

Welcome back to the fold.



I should be continuing these shortly into the new year :devil:

I can do the Mersenne cofactor Ryan reserved about a year ago too. Ryan?
Forum: And now for something completely different 2021-11-28, 07:42
Replies: 13
Views: 7,430
Posted By paulunderwood
Playing the sleuth, I think I can answer this....

Playing the sleuth, I think I can answer this. Putting "Gleit kommarechnerheizgerät" in to google translate gives "Sliding comma computer heater". The German people often concatenate their written...
Forum: Hardware 2021-11-27, 21:34
Replies: 224
Views: 37,509
Posted By paulunderwood
Thumbs up Formidable power. I had toyed with getting such a...

Formidable power. I had toyed with getting such a system. The potential noise put me off. It would draw about 1400w running flat out. One would need a garage or basement to house it. I think it is...
Forum: Math 2021-11-27, 09:22
Replies: 8
Views: 201
Posted By paulunderwood
It is not so great since (3/2)^2-2 = 1/4 which is...

It is not so great since (3/2)^2-2 = 1/4 which is already known.

Just as (3)^((Mp - 1)/2) == -1 mod Mp for Mersenne primes, we have (-7)^((Wq - 1)/2) == 1 mod Wq for Wagstaff PRPs. The latter can...
Forum: Math 2021-11-26, 23:49
Replies: 8
Views: 201
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: 8
Views: 201
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: 20,444
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: 5,605
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: 7
Views: 455
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: 7
Views: 455
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: 5,605
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: 659
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: 1,326
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: 59
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: 27,469
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: 685
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: 9,282
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: 9,282
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: 5,605
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: 5,605
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: 5,605
Posted By paulunderwood
Has it been initialized?

Has it been initialized?
Forum: Number Theory Discussion Group 2021-11-13, 20:08
Replies: 30
Views: 5,605
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?
Showing results 1 to 25 of 1000

 
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