mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 355
Search took 0.05 seconds.
Search: Posts Made By: bhelmes
Forum: Factoring 2021-10-13, 17:28
Replies: 0
Views: 263
Posted By bhelmes
a variation of pollard rho

A peaceful and pleasant night for you,

I present a variation of a pollard rho algorithm, limited to Mp, with use of a solution of the pell equation x²-2y²=-1.

Easy to understand and short for...
Forum: Number Theory Discussion Group 2021-09-23, 00:35
Replies: 2
Views: 850
Posted By bhelmes
A peaceful night for you, The last program...

A peaceful night for you,

The last program was too slow. I am thinking of using the chinese remainder theorem in order to search for a factor of Mp.

I would suggest a linear substitution for...
Forum: Number Theory Discussion Group 2021-09-15, 23:15
Replies: 2
Views: 850
Posted By bhelmes
A peaceful and pleasant night for you, I...

A peaceful and pleasant night for you,

I have successfully implemented the following algorithm:

1. precalculate primes and n with help of f(n)=2n²-1
2. make a linear substitution with...
Forum: Number Theory Discussion Group 2021-09-09, 23:05
Replies: 2
Views: 850
Posted By bhelmes
speed up by a linear substitution of a quadratic polynomial ?

A peaceful and pleasant day for you,

Let f(n)=2n²-1 and the linear substitution n=Mp*k+1, Mp is the exponent of the coresponding Mersenne number

I know that there is a factor g | f(n0) if...
Forum: Number Theory Discussion Group 2021-09-04, 21:29
Replies: 21
Views: 1,464
Posted By bhelmes
The statement was not exactly formulated : ...

The statement was not exactly formulated :

if f>1 is the smallest factor of a Mersenne number, than there exists a n0>1 for the function f(n)=2n²-1
where n0 is the minimum, so that f | f(n0) and...
Forum: Number Theory Discussion Group 2021-09-03, 00:51
Replies: 21
Views: 1,464
Posted By bhelmes
factors of Mersenne numbers

A peaceful and pleasant night for you,

if f>1 is the smallest factor of a Mersenne number, than there exists a n0>1 for the function f(n)=2n²-1
where n0 is the minimum, so that f | f(n0) and...
Forum: Dobri 2021-08-26, 20:14
Replies: 50
Views: 2,079
Posted By bhelmes
Perhaps this is helpful for you: p 1 ...

Perhaps this is helpful for you:

p 1 3 5 mod 6
------------------
10 1 1 1
10^2 11 1 12
10^3 80 1 86
10^4 611 1 616
10^5 4784 1 ...
Forum: Hardware 2021-08-10, 17:06
Replies: 23
Views: 2,047
Posted By bhelmes
A peaceful and pleasant day for you, I...

A peaceful and pleasant day for you,

I thought of adding a nvidia geforce 1030 card (passiv, 30 Watt) and use cudalucas instead of mprime.
The cpu (Ryzan 3600) use ca. 110 Watt, and the computer...
Forum: Number Theory Discussion Group 2021-07-29, 20:09
Replies: 3
Views: 534
Posted By bhelmes
(p = a(x1)²+b(x1)+c) && (q = A(x1)²+B(x1)+C)

@Dr Sardonicus

It is always illuminating and friendly getting a response from you, thanks a lot for your clear and precious words. :hello:

If p(x1)=a(x1)²+b(x1)+c and
If q(x1)=A(x1)²+B(x1)+C...
Forum: Number Theory Discussion Group 2021-07-28, 00:51
Replies: 3
Views: 534
Posted By bhelmes
(p | ax²+bx+c) && (p | Ax²+Bx+C)

A peaceful night for you,

Let f(x)=ax²+bx+c and g(x)=Ax²+Bx+C with discriminant (f(x))=/=discr (g(x)) and f(x0)=g(x0)

I am looking for a prime p>2 where p | f(x1) and p | g(x1)

Is there a...
Forum: Miscellaneous Math 2021-07-14, 23:29
Replies: 5
Views: 1,003
Posted By bhelmes
This was wrong, I have implemented this idea, but...

This was wrong, I have implemented this idea, but the primes generating by the polynomial f(n)=2n²-1 do not "cover" completely the resulting quadratic polynomial. I think a sieve of Eratosthenes will...
Forum: Number Theory Discussion Group 2021-07-09, 20:32
Replies: 9
Views: 1,024
Posted By bhelmes
@Nick, thanks a lot for your work and help. ...

@Nick, thanks a lot for your work and help.

an useful implementation in c and gmp of tonelli-shanks algorithm is:
http://www.codecodex.com/wiki/Shanks-Tonelli_algorithm


Let :...
Forum: Number Theory Discussion Group 2021-07-08, 21:18
Replies: 9
Views: 1,024
Posted By bhelmes
Let an²+bn+c = 0 mod p If I want to...

Let an²+bn+c = 0 mod p

If I want to calculate the discriminant,
can I first calculate a*=a mod p, b*=b mod p and c*=c mod p
and then discr=(b*)²-4a*c* ?
Forum: Number Theory Discussion Group 2021-07-07, 02:56
Replies: 9
Views: 1,024
Posted By bhelmes
I did not understand how to find the square of...

I did not understand how to find the square of the discriminant b²-4ac mod 4an.
b²-4ac is a quadratic residue, but not always a square.
:loco:
Forum: Number Theory Discussion Group 2021-07-05, 19:24
Replies: 9
Views: 1,024
Posted By bhelmes
an²+bn+c = 0 mod p

Let f(n)=an²+bn+c = 0 mod p
with n element of N and p prime.
n=?

Is there a better way than calculating f(n) for n=0 ...p-1

Thanks if you spend me some lines.
Forum: Miscellaneous Math 2021-06-30, 00:14
Replies: 5
Views: 1,003
Posted By bhelmes
A peaceful night for you, I try to describe...

A peaceful night for you,

I try to describe a possible trial factor algorithm for mps:

0. Consider one mp.
1. Generate 10^9 primes and the n0 from the polynomial f(n)=2n²-1
2. Make a linear...
Forum: Miscellaneous Math 2021-06-29, 01:21
Replies: 2
Views: 343
Posted By bhelmes
A friendly good night for you Let f(n)=2n²-1...

A friendly good night for you

Let f(n)=2n²-1 and t|f(no)
g(k)=2k²-1 - C where C is a constant
for which k0 t|g(ko) ?

this is not a linear substitution and I will be glad knowing the answer....
Forum: Miscellaneous Math 2021-06-27, 18:31
Replies: 2
Views: 343
Posted By bhelmes
Solving the linear substitution to k will do it. ...

Solving the linear substitution to k will do it.
:brian-e: :geek: :beer:
Forum: Miscellaneous Math 2021-06-26, 23:00
Replies: 2
Views: 343
Posted By bhelmes
lineare substitution

A peaceful and pleasant night for you,

Let f(n)=2n²-1 n=a+bk
then f(a+bk)=2(a+bk)²-1= 2(a²+2abk+b²k²)=2a²+4abk+2b²k²=g(k)

if t|f(n) for which k t|g(k) ?

I am today a little bit stupid...
Forum: Number Theory Discussion Group 2021-06-20, 00:24
Replies: 10
Views: 2,017
Posted By bhelmes
A peaceful and pleasant night for you, For...

A peaceful and pleasant night for you,

For people who like php-scripts I added a calculator which decline from the pyth. trippel to the gaussian integer modulo f:
...
Forum: Number Theory Discussion Group 2021-06-11, 02:32
Replies: 10
Views: 2,017
Posted By bhelmes
Thanks a lot for all replies. :hello: Is...

Thanks a lot for all replies. :hello:

Is this a mathematical correct way:

1. Choose a,b with a>0 and b>0 and a=/=b and a²+b² =/=0 mod f
(the trivial solutions are not important for me)

2....
Forum: Number Theory Discussion Group 2021-06-10, 00:44
Replies: 10
Views: 2,017
Posted By bhelmes
how do I find a and b with a²+b²=1 mod f

A peaceful and pleasant night for you,

how do I find (fast ?) a gaussian number a+bi with a²+b²=1 mod f
where f is an odd number.

Perhaps this question might be interesting also for others. ...
Forum: Miscellaneous Math 2021-06-07, 00:43
Replies: 0
Views: 192
Posted By bhelmes
was: a deterministic test for primes p=1 or p=7 mod 8 with 2 Selfridges

A peaceful and pleasant night for you,

the counter example of the last test was wrong.

There is a difference in the complex calculation:
If you use a factor=gcd (a,b) from a+bi and define...
Forum: Hardware 2021-06-06, 18:50
Replies: 23
Views: 2,047
Posted By bhelmes
I tried several possibilities in the Bios. All in...

I tried several possibilities in the Bios. All in all there is not much progress.
I think, I will run 200 DCs this year and switch off the computer in the hot season.
Thanks for your replys.

...
Forum: Miscellaneous Math 2021-06-02, 20:25
Replies: 10
Views: 2,509
Posted By bhelmes
You can visualize gaussian numers in two...

You can visualize gaussian numers in two different ways:

1. Reducing it to the unit circle, so that the norm (a,b)=a²+b²= 1 mod p
http://devalco.de/unit_circle/system_unit_circle.php?prim=127
...
Showing results 1 to 25 of 355

 
All times are UTC. The time now is 10:23.


Wed Oct 20 10:23:00 UTC 2021 up 89 days, 4:51, 0 users, load averages: 1.08, 1.60, 1.82

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.