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Forum: Miscellaneous Math 2020-08-09, 15:49
Replies: 27
Views: 2,289
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: 27
Views: 2,289
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: 27
Views: 2,289
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: 126
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: 27
Views: 2,289
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: 27
Views: 2,289
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: 27
Views: 2,289
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
Forum: Miscellaneous Math 2020-05-09, 18:56
Replies: 27
Views: 2,289
Posted By bhelmes
if p=x²+1 then x | p-1 if p | (x²+1) ???...

if p=x²+1 then x | p-1


if p | (x²+1) ???


Can I calculate q=x²+1 with q=r*p and x and r known; then f | p-1 ; f ???


If someone knows a good answer would be very nice to get it.
Forum: Miscellaneous Math 2020-05-07, 21:47
Replies: 27
Views: 2,289
Posted By bhelmes
A peaceful and pleasant night for you, if...

A peaceful and pleasant night for you,


if I regard only the primes p>=5 with p=x²+1 (x>1) and
the primes p with p | (x²+1 ) with p > x


can i derive any suggestion about the factorisation...
Forum: Software 2020-04-30, 20:21
Replies: 2
Views: 553
Posted By bhelmes
g++ -O3 -std=c++0x -pthread -mcmodel=medium...

g++ -O3 -std=c++0x -pthread -mcmodel=medium -pedantic ./2x^2-1_220.cpp -l gmp /usr/local/lib/libgmp.a -lecm /usr/local/lib/libecm.a

will do it.
Forum: Software 2020-04-30, 16:29
Replies: 2
Views: 553
Posted By bhelmes
error with gmp-ecm library

A peaceful and pleasant day for you,


i have installed gmp-6.2.0 and ecm-7.0.4 and i want to use the ecm-library for an own program with :


g++ -O3 -std=c++0x -pthread -lecm -mcmodel=medium...
Forum: Miscellaneous Math 2020-04-12, 19:23
Replies: 97
Views: 9,238
Posted By bhelmes
You know how you motivate persons, but you are...

You know how you motivate persons, but you are right:


there is a small table with n=40 up to n=46.
I did not check the whole range.
but nevertheless the program gives correct (known) factors....
Forum: Miscellaneous Math 2020-04-02, 20:14
Replies: 97
Views: 9,238
Posted By bhelmes
how many factors I will find ? Give a...

how many factors I will find ?


Give a number, :cmd: :brian-e: :truck:



P.s. I don't think it is a random distribution
Forum: Miscellaneous Math 2020-03-28, 17:29
Replies: 97
Views: 9,238
Posted By bhelmes
A peaceful day for you, if I sieve the...

A peaceful day for you,

if I sieve the function f(n)=2n²-1 up to n=2^40,
save all primes < 2^40 (~ 10^10 primes)
jump to n=2^45,
transform the saved primes for the limit n=2^45
and sieve the...
Forum: Math 2020-03-19, 22:14
Replies: 21
Views: 3,716
Posted By bhelmes
@sm You are not able to see the beauty of...

@sm


You are not able to see the beauty of the described algorithms,
nor you could appreciate a piece of mathematic,
which may be not quite perfect.


Do all famous mathematicians get grumpy...
Forum: Math 2020-03-17, 21:01
Replies: 21
Views: 3,716
Posted By bhelmes
A peaceful and pleasant day, may be...

A peaceful and pleasant day,


may be someone has time and fun to read my book about prime generators for irreducible quadratic polynomials.


http://devalco.de/quadratic_prime_sieves.pdf

...
Forum: Miscellaneous Math 2020-03-04, 20:52
Replies: 2
Views: 1,406
Posted By bhelmes
It is always possible to reduce the 2x2...

It is always possible to reduce the 2x2 bilinearform to a quadratic polynom
by setting y=x, this is trivial.


If I choose a linear substituion for y depending on x (for example y=2x)
can i make...
Forum: Miscellaneous Math 2020-02-26, 19:46
Replies: 2
Views: 1,406
Posted By bhelmes
this was mathematical nonsens: if A is the...

this was mathematical nonsens:
if A is the matrix of the bilinearform and v the eigenvektor,
than Av=rv, multiplication with the vektor v on the left side gives the result
vAv=v*r*v = r *v *v...
Forum: Miscellaneous Math 2020-02-21, 20:08
Replies: 2
Views: 1,406
Posted By bhelmes
pollard rho with bilinear form and eigenvektor ?

A peaceful evening,


if i make a pollard rho algorithm with a suitable bilinear form instead

of the function f(x)=x²+1, is it then better to use the eigenvektor of the matrix or not.


I...
Forum: Computer Science & Computational Number Theory 2020-02-03, 20:58
Replies: 17
Views: 1,322
Posted By bhelmes
A peaceful and pleasant night for you, ...

A peaceful and pleasant night for you,


there are some fresh results for the polynom f(n)=n²+1 up to n<2^40:


http://devalco.de/quadr_Sieb_x%5E2+1.php#4g


calculation was done in 104h.
Forum: Miscellaneous Math 2020-01-07, 16:04
Replies: 10
Views: 829
Posted By bhelmes
A peaceful evening for you, it might be...

A peaceful evening for you,


it might be better to use a quadratic binary form f(x,y) and derive the squaring function by the resulting f(x,x) and make then a fast exponentation by using these...
Forum: Miscellaneous Math 2020-01-04, 12:20
Replies: 10
Views: 829
Posted By bhelmes
Thank you for your friendly lines, I appreciate...

Thank you for your friendly lines, I appreciate your clear and benevolent style of writing.


I am playing with some factorisation algorithms and use the binary exponentation function, which...
Forum: Miscellaneous Math 2020-01-03, 15:21
Replies: 10
Views: 829
Posted By bhelmes
A peaceful day for you, 1. Let p=7 ...

A peaceful day for you,


1. Let p=7 2^(p-1)= 1 mod 7 (little lemma from Fermat)


2. Define x²:=x²+1 Let p=7 2^7 = 2^(lll) =2*2²*2⁴ (lll should be the binary representation)
...
Forum: Miscellaneous Math 2020-01-02, 23:02
Replies: 10
Views: 829
Posted By bhelmes
Redefining Fermat's little theorem

A peaceful and pleasant night for you,


If i substitute the normal multiplication by an quadratic irreducible polynom
like x*x := x*x+1 is the little fermat theorem still right ?


If someone...
Forum: Computer Science & Computational Number Theory 2019-12-18, 23:22
Replies: 17
Views: 1,322
Posted By bhelmes
Thanks for the reply and the precise explication,...

Thanks for the reply and the precise explication, Dr Sardonicus


If i regard the polynomial f(n)=n²+1 for n element N
then this polynomial has the property that there is always only one new...
Showing results 1 to 25 of 257

 
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