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 Showing results 1 to 25 of 288 Search took 0.05 seconds. Search: Posts Made By: bhelmes
 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:
 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.
 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
 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 ......
 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
 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...
 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.
 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
 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 ...
 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) =...
 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...
 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
 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...
 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)
 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:
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