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Search: Posts Made By: bhelmes
Forum: Number Theory Discussion Group 2021-01-24, 02:51
Replies: 2
Views: 302
Posted By bhelmes
A peaceful and pleasant night, what is the...

A peaceful and pleasant night,

what is the difference between eliptic curves and quadratic polynomials,
resp. what mathematical property does eliptic curves have in opposite to quadratic...
Forum: Soap Box 2021-01-17, 23:10
Replies: 2
Views: 227
Posted By bhelmes
best crackpot message in 2020

For a little bit entertainment:


What message of Misc.Math was your personal crackpot-winner according
http://primes.utm.edu/notes/crackpot.html (http://primes.utm.edu/notes/crackpot.html) in...
Forum: Miscellaneous Math 2021-01-05, 01:58
Replies: 9
Views: 237
Posted By bhelmes
I get other values and you could visualize them: ...

I get other values and you could visualize them:
http://devalco.de/System/system_natural.php?prim=2047
Forum: Number Theory Discussion Group 2021-01-05, 01:42
Replies: 2
Views: 302
Posted By bhelmes
special quadratic polynomials : f(n)=an²+bn+1

A peaceful night for you,


I noticed for some quadratic polynomial, such as f(n)=n²+1, f(n)=2n²-1, f(n)=2n²+1 and f(n)=4n²+1 you can make a linear substitution with n=p*k+n0 with p|f(n) and...
Forum: Number Theory Discussion Group 2021-01-01, 21:00
Replies: 1
Views: 192
Posted By bhelmes
a p+1 factoring test for Mp ?

A peaceful and pleasent new year 2021,


Is a p+1 factoring test for Mp possible or not ?

You could use complex numbers and make a similar factoring test like p-1.

In the section math there...
Forum: Number Theory Discussion Group 2020-12-26, 01:48
Replies: 8
Views: 461
Posted By bhelmes
It is always a pleasure to read your clear...

It is always a pleasure to read your clear explications, many thanks for your support.


I am still missing the next Mersenne Prime number,

by all the amazing amount of work in 2020 there will...
Forum: Number Theory Discussion Group 2020-12-20, 03:31
Replies: 8
Views: 461
Posted By bhelmes
rational points on the unit circle

A peaceful and pleasant night for you,


I found the text in the english Wikipedia:
https://en.wikipedia.org/wiki/Group_of_rational_points_on_the_unit_circle#Group_structure


I did not...
Forum: Number Theory Discussion Group 2020-12-16, 02:28
Replies: 1
Views: 172
Posted By bhelmes
a prime sieve for f(n)=n⁴+1

A peaceful night,


the sieve algorithm for the function f(n)=2n²-1 was too slow,
even with some improvements.


The function f(n)=n^p-1 increase too fast for practical use.
Forum: Hardware 2020-12-08, 04:27
Replies: 0
Views: 332
Posted By bhelmes
hardware donation : 4*8Gb Ecc ram

A peacefull time in the advent,


I have 4*8 Gb Samsung 2Rx3 PC-3 10600R-09-10-E1-P1
M393B1K70CH0-CH9 and will send it as present for someone


I could not check the Rams, because I have no...
Forum: Number Theory Discussion Group 2020-12-02, 00:39
Replies: 10
Views: 1,030
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: 1,801
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: 584
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: 416
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: 1,030
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: 1,030
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: 1,030
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: 1,040
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: 1,040
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: 1,040
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: 1,040
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: 1,040
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: 1,040
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: 650
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: 1,732
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: 8,298
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...
Showing results 1 to 25 of 297

 
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