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Search: Posts Made By: bhelmes
Forum: Number Theory Discussion Group 2020-10-16, 19:44
Replies: 3
Views: 104
Posted By bhelmes
runtime for the calculation of a quadratic residue

A peaceful and pleasant day for you,

What is the runtime of the jacobi / legendre / kronecker function
in order to determine wether x is a quadratic residue concerning
the prime p.

Is this...
Forum: Miscellaneous Math 2020-10-10, 20:46
Replies: 18
Views: 691
Posted By bhelmes
"It is important to analize the the...

"It is important to analize the the exponentiating" page 49.


Greetings
Bernhard
Forum: Miscellaneous Math 2020-10-08, 11:23
Replies: 31
Views: 3,939
Posted By bhelmes
A peaceful day, this is the end of a...

A peaceful day,


this is the end of a wonderful programming episode:
Running of the program was only one day,
I used 59 GByte Ram for storing the sieving primes,
used ecm-library and a...
Forum: Number Theory Discussion Group 2020-10-03, 17:03
Replies: 4
Views: 259
Posted By bhelmes
Most people know the 9-rule in the decimalsystem ...

Most people know the 9-rule in the decimalsystem
which based on the fact that 10 = 1 mod 9


For Mersenne numbers it is the same reflection
that 2^p = 1 mod 2^p -1
Forum: Number Theory Discussion Group 2020-10-02, 20:22
Replies: 4
Views: 259
Posted By bhelmes
calculation of modulo Mp

A peaceful and pleasant day for you,


I do not understand how the calculation modulo a Mersenne prime is made:


https://en.wikipedia.org/wiki/Mersenne_prime:
"Arithmetic modulo a Mersenne...
Forum: Number Theory Discussion Group 2020-09-30, 17:38
Replies: 3
Views: 254
Posted By bhelmes
A peaceful night for you, you are right,...

A peaceful night for you,


you are right, but this is not really new for me.


You can transform the polynom for pollard rho in a 2x2 matrix
and calculate the 2x2 matrix with fast...
Forum: Miscellaneous Math 2020-09-29, 22:05
Replies: 31
Views: 3,939
Posted By bhelmes
A peaceful and pleasant night for you, I...

A peaceful and pleasant night for you,


I have primes p ~ 120 bits big,

I want to factorize p-1,
I do a f=gcd (8*9*25*7*11*13*17*19*23*29*31*37*41, p-1) and
check wether 2^[(p-1)/f]=1 mod p...
Forum: Hardware 2020-09-19, 21:45
Replies: 10
Views: 647
Posted By bhelmes
It is not possible. I have an Asus motherboard...

It is not possible.
I have an Asus motherboard 450 Plus and if a M.2 card is installed,
the bios cut the 5. and 6. ssd disks.


I will "experimentieren" a little bit with the M.2 card,
I use it...
Forum: Miscellaneous Math 2020-09-14, 17:36
Replies: 8
Views: 444
Posted By bhelmes
You did not understand the algorithm. Have a...

You did not understand the algorithm.
Have a look at :
http://devalco.de/quadr_Sieb_2x%5E2-1.php


I improved the page and hope that the content is well described,
if you have improvements,...
Forum: Miscellaneous Math 2020-09-13, 04:53
Replies: 8
Views: 444
Posted By bhelmes
f should be a proper divisor from the non prime...

f should be a proper divisor from the non prime Mp,
where Mp is a Mersenne number with prime p.
Forum: Miscellaneous Math 2020-09-11, 23:00
Replies: 8
Views: 444
Posted By bhelmes
factors of Mersenne numbers

If f | Mp and p is prime then

a) f | 2n²-1

b) but not f=2n²-1


a) is clear for me but b) is a guess (I checked some numbers)
Forum: Number Theory Discussion Group 2020-09-09, 18:31
Replies: 3
Views: 405
Posted By bhelmes
Thanks for this clear answer. :hello: :cmd: ...

Thanks for this clear answer. :hello: :cmd: :pals:
Forum: Number Theory Discussion Group 2020-09-09, 02:50
Replies: 3
Views: 405
Posted By bhelmes
f(x,y)=x²+y², g(x,y)=x²-2y², h(x,y)=?

A peaceful night for you,


I am looking for the third biquadratic function,
so that all primes are "covered" by these three functions.


There is a relationship concerning the pyth. triples....
Forum: Hardware 2020-09-09, 00:56
Replies: 10
Views: 647
Posted By bhelmes
Generally, I want to write and read on one bigger...

Generally, I want to write and read on one bigger divice in a RAID 0 array,
where the average time to write and read is better than a solid device.


I have one program which is greedy concerning...
Forum: Hardware 2020-09-07, 18:06
Replies: 10
Views: 647
Posted By bhelmes
A peaceful day for you, as far as I...

A peaceful day for you,


as far as I understand, linux regard the ssd-disk as a device and the M.2 also.
The difference in speed may be small,

the ssd-disks are pluged by the sata-bus, the...
Forum: Hardware 2020-09-06, 19:50
Replies: 10
Views: 647
Posted By bhelmes
integrating M.2 card in raid0 system

I have 6 ssd disks, combined to a raid 0 system.
Can I add a M.2 card in addition ?


I have a linux mint system and I thought of increasing speed and huge.



Greetings :brian-e:
Forum: Miscellaneous Math 2020-08-28, 20:35
Replies: 31
Views: 3,939
Posted By bhelmes
I have some datas up to 2^40 for the primesieving...

I have some datas up to 2^40 for the primesieving for the polynomial

f(n)=2n²-1;
http://devalco.de/quadr_Sieb_2x%5E2-1.php#4a


I think the density of "non reducible primes" (p=f(n))
is an...
Forum: Combinatorics & Combinatorial Number Theory 2020-08-14, 21:44
Replies: 5
Views: 1,433
Posted By bhelmes
is the factorisation of Mp-1 an advantage ?

A peaceful and pleasant night for you,


if I know the factorisation or a part of the factorisation of Mp-1
do I have any advantages for checking the primality ?


(Mp should be a Mersenne...
Forum: Miscellaneous Math 2020-08-09, 15:49
Replies: 31
Views: 3,939
Posted By bhelmes
A peaceful day for you, LaurV ...

A peaceful day for you, LaurV






I think I will use the function f(n)=2n²-1 from n=1 up to 2^40,
will calculating the factors / primes f(m) with f>m and will storing the m for each f, will...
Forum: Miscellaneous Math 2020-07-21, 22:54
Replies: 31
Views: 3,939
Posted By bhelmes
In general : let f(n)=2n²-1 f(n0)=r ...

In general :

let f(n)=2n²-1

f(n0)=r

then the substitution is n=f(n0)*k+n0 with the following division by f(n0)


I think I will combine the sieving algorithm with the prediction by adding...
Forum: Miscellaneous Math 2020-07-20, 20:20
Replies: 31
Views: 3,939
Posted By bhelmes
A peaceful evening for you, perhaps my...

A peaceful evening for you,

perhaps my mathematical skill is not the best in explaining,
but i am sure that the math behind it is right.

Therefore I try again to explain it and will give an...
Forum: Miscellaneous Math 2020-07-13, 17:58
Replies: 0
Views: 472
Posted By bhelmes
quadratic reciprocity law for gaussian integer and pyth. triple

A peaceful evening for you,


I noticed that there exists a quadratic reciprocity law for gaussian integers:
https://en.wikipedia.org/wiki/Quadra...ssian_integers...
Forum: Miscellaneous Math 2020-05-21, 08:58
Replies: 31
Views: 3,939
Posted By bhelmes
A peaceful day for you, LaurV who should...

A peaceful day for you, LaurV


who should type a 20 digits example ?

I will give a second example which is working:


f(n)=n²+1
f(92)=5*1693
Forum: Miscellaneous Math 2020-05-20, 20:07
Replies: 31
Views: 3,939
Posted By bhelmes
A peaceful and pleasant night for you, ...

A peaceful and pleasant night for you,

Perhaps I should explain the algorithm and the solution a little bit better.


I have the factorisation of
f(n)=n²+1=r*p where r element of N and p is...
Forum: Miscellaneous Math 2020-05-16, 20:04
Replies: 31
Views: 3,939
Posted By bhelmes
A peaceful and pleasant night for you, ...

A peaceful and pleasant night for you,




Yes, there is a mathematical possibility:


f(x)=x²+1
f(27)=10*73
Showing results 1 to 25 of 275

 
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