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Forum: Number Theory Discussion Group 2020-12-02, 00:39
Replies: 10
Views: 578
Posted By bhelmes
(2(k*p + r)^2 - 1)/p = 2p*k^2 + 4*k*r + (2r^2 -...

(2(k*p + r)^2 - 1)/p = 2p*k^2 + 4*k*r + (2r^2 - 1)/p


If I choose a linear substitution with p=2n²-1 and the same n,
so that m=k*p+n then I will always get a quadratic polynomial like...
Forum: ONeil 2020-11-15, 21:40
Replies: 48
Views: 1,106
Posted By bhelmes
m = (2**p-1) prime = ((m + m)%p) how about...

m = (2**p-1)
prime = ((m + m)%p) how about fast exponention modulo p, described in
http://rosettacode.org/wiki/Modular_exponentiation
Forum: Hardware 2020-11-15, 19:03
Replies: 1
Views: 181
Posted By bhelmes
my christmas tree and computer for Gimps

Looks nice, a headless computer, most for Gimps, and maybe a religious touch
Forum: Miscellaneous Math 2020-11-13, 21:40
Replies: 1
Views: 141
Posted By bhelmes
(a/b) mod p ?

What is the fastest way to calculate a rational number a/b with a, b element N and gcd (b,p)=1 mod p where the result is in N ? :geek: :uncwilly: :gah:
Forum: Number Theory Discussion Group 2020-11-12, 01:52
Replies: 10
Views: 578
Posted By bhelmes
Exact right I am trying to...

Exact right






I am trying to parallize the algorithm and to improve the runtime.
Forum: Number Theory Discussion Group 2020-11-10, 16:14
Replies: 10
Views: 578
Posted By bhelmes
Dear Dr Sardonicus The first...

Dear Dr Sardonicus






The first prime p concerning the polynomial f(n)=2n²-1 (with p|f(n)) are
Forum: Number Theory Discussion Group 2020-11-08, 17:43
Replies: 10
Views: 578
Posted By bhelmes
linear substitution and sieving

A peaceful and pleasant day for you,


I have a sieving construction for f(n)=2n²-1,
(that means that every prime p with p | f(n) sieves at two n1 and n2 periodically with p the field for n=0 ......
Forum: Number Theory Discussion Group 2020-11-02, 20:28
Replies: 12
Views: 548
Posted By bhelmes
alpha=arctan (1/11)=5,194428908 sin...

alpha=arctan (1/11)=5,194428908


sin (alpha)=0,090535746
61²*sin (alpha)=336,883511024
337 =32 mod 61 = 29 mod 61



cos (alpha)=0,995893206
Forum: Number Theory Discussion Group 2020-11-02, 18:40
Replies: 12
Views: 548
Posted By bhelmes
For mathematical curosity and practical use: ...

For mathematical curosity and practical use:


Is it possible to calculate the square root of a quadratic residium by using the tangens function ?


I have the pythagoraic tripple 11,60,61...
Forum: Number Theory Discussion Group 2020-11-01, 20:00
Replies: 12
Views: 548
Posted By bhelmes
How do you calculate the mapping function ? ...

How do you calculate the mapping function ?


Thanks for your clear explications.
Forum: Number Theory Discussion Group 2020-11-01, 09:25
Replies: 12
Views: 548
Posted By bhelmes
??? I think 61 is a prime ideal in the Gaussian...

???
I think 61 is a prime ideal in the Gaussian integers,
61=(6+5i)(6-5i)



http://devalco.de/poly_xx+yy_demo.php?radius_a=11&radius_b=60&radius_c=61


I understand that -i²=1
Forum: Number Theory Discussion Group 2020-10-31, 18:57
Replies: 12
Views: 548
Posted By bhelmes
(16+29i)²=(25+13i) mod 61 (25+13i) can be...

(16+29i)²=(25+13i) mod 61
(25+13i) can be mirrored at the main diagonale,
so that the point of the unit circle (13+25i) "=" (25+13i)


tan (alpha)=3/4, tan (alpha/2)=(5-4)/3=1/3 if this helps
...
Forum: Number Theory Discussion Group 2020-10-31, 03:35
Replies: 12
Views: 548
Posted By bhelmes
calculation of the non quadratic residium

A peaceful and pleasant night for you,


I know that from the pyth. trippel (3, 4, 5) - > 3/5, 4/5 mod 61 = (13+25i)

1. and that (13+25i)^30 = 1 mod 61
2. and |16+29i| = (16²+29²) =...
Forum: Number Theory Discussion Group 2020-10-16, 19:44
Replies: 3
Views: 318
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: 1,084
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: 5,581
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: 586
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: 586
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: 484
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: 5,581
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: 1,139
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: 848
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: 848
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: 848
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: 848
Posted By bhelmes
Thanks for this clear answer. :hello: :cmd: ...

Thanks for this clear answer. :hello: :cmd: :pals:
Showing results 1 to 25 of 288

 
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