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Forum: Number Theory Discussion Group 2021-11-22, 22:59
Replies: 0
Views: 80
Posted By bhelmes
searching a factor with a bilinear form

A peaceful and pleasant night,

I am missing a little bit the sunshine, november in Germany is not the best time.

If I have a bilinear form mod f such as
(a b)
(b d)

a, b, d elements of N
Forum: Homework Help 2021-11-19, 19:05
Replies: 1
Views: 133
Posted By bhelmes
factorisation with help of 2*2 matrix

A peaceful day,

I am a little bit struggled:

If M is a 2*2 matrix of the form
(a, b)
(b, d)

Let M²=E mod f, then there should be a factorisation possible:
Forum: Number Theory Discussion Group 2021-11-15, 17:33
Replies: 30
Views: 5,726
Posted By bhelmes
Something is boogie: I used my variable a...

Something is boogie:


I used my variable a and put it in your solution:

Result is wrong:


137 is exponent.
Mp is 174224571863520493293247799005065324265471.
Forum: Number Theory Discussion Group 2021-11-13, 22:24
Replies: 30
Views: 5,726
Posted By bhelmes
In gmp I could use the same mpz_t variable A like...

In gmp I could use the same mpz_t variable A like mpz_mod (A, A, f);
I tried to write a function like this mpz_mod_mp (A, A, Mp), therefore I initialized a help variable.

Thanks for your patience.
Forum: Number Theory Discussion Group 2021-11-13, 20:46
Replies: 30
Views: 5,726
Posted By bhelmes
That was a logical error, a<>0, the do loop is...

That was a logical error, a<>0, the do loop is entered and by chance a=0 for mpz_fdiv_q_2exp (a, a, mp);

f=174224571863520493293247799005065324265471
and p=137 by the way.

We are approaching...
Forum: Number Theory Discussion Group 2021-11-13, 20:01
Replies: 30
Views: 5,726
Posted By bhelmes
for a=0 the loop with mpz_sizeinbase is not...

for a=0 the loop with mpz_sizeinbase is not entered.
Forum: Number Theory Discussion Group 2021-11-13, 19:44
Replies: 30
Views: 5,726
Posted By bhelmes
I need for the function mpz_fdiv_r_2exp the...

I need for the function mpz_fdiv_r_2exp the variable as mp_bitcnt_t, therefore I made a change from uint_64 to mp_bitcnt_t


f is Mp as mpz_t variable

But why is res_1 and res_2 not equal 0 ?...
Forum: Number Theory Discussion Group 2021-11-13, 19:11
Replies: 30
Views: 5,726
Posted By bhelmes
A peaceful and pleasant day for you, there...

A peaceful and pleasant day for you,

there is a bug in the function, and I have no idea, where the reason is:


void mpz_mod_mp (mpz_t r, mpz_t a, uint64 p)
{
mpz_t res_1, res_2;
...
Forum: MattcAnderson 2021-11-12, 21:28
Replies: 11
Views: 349
Posted By bhelmes
I think the existence of prime numbers has...

I think the existence of prime numbers has started one nanosecond before time has started.

:blush: :geek: :redface:
Forum: Number Theory Discussion Group 2021-11-12, 16:36
Replies: 16
Views: 2,684
Posted By bhelmes
A peaceful day for you, The time function, I...

A peaceful day for you,

The time function, I used, was wrong. I have changed that bug and can prove that the test is not a p-1 or p+1 test with help of the chinese remainder theorem...
Forum: Number Theory Discussion Group 2021-11-03, 17:52
Replies: 30
Views: 5,726
Posted By bhelmes
nice stroke, Mp was uint64, p was mp_bitcnt_t. ...

nice stroke, Mp was uint64, p was mp_bitcnt_t.
I replaced the mp_bitcnt_t by uint64 and the results are correct.
Thanks a lot.


:smile:
Forum: Number Theory Discussion Group 2021-11-03, 17:39
Replies: 30
Views: 5,726
Posted By bhelmes
yes, otherwise the program would not run.

yes, otherwise the program would not run.
Forum: Number Theory Discussion Group 2021-11-03, 17:24
Replies: 30
Views: 5,726
Posted By bhelmes
I had some problems to use the function,...

I had some problems to use the function, described before, mpz_mod_Mp


void mpz_mod_mp (mpz_t r, mpz_t a, mp_bitcnt_t p)
{
mpz_t res;
mpz_init (res);

// assumed that r is...
Forum: Number Theory Discussion Group 2021-10-23, 21:49
Replies: 2
Views: 405
Posted By bhelmes
2*2 Matrix with determinant 1

A peaceful night for you,

do I see it right that 2*2 matrix with determinant 1 build a subgroup in linear algebra
and that calculation in the group is better for factoring than calculation in all...
Forum: Factoring 2021-10-13, 17:28
Replies: 2
Views: 626
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: 1,066
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: 1,066
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: 1,066
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: 1,865
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: 1,865
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: 2,555
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: 2,336
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: 659
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: 659
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: 1,107
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...
Showing results 1 to 25 of 369

 
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