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 Showing results 1 to 25 of 257 Search took 0.06 seconds. Search: Posts Made By: bhelmes
 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...
 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...
 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...
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