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 Showing results 1 to 25 of 355 Search took 0.05 seconds. Search: Posts Made By: bhelmes
 Forum: Factoring 2021-10-13, 17:28 Replies: 0 a variation of pollard rho Views: 263 Posted By bhelmes a variation of pollard rho A peaceful and pleasant night for you, I present a variation of a pollard rho algorithm, limited to Mp, with use of a solution of the pell equation x²-2y²=-1. Easy to understand and short for... 2021-09-23, 00:35 Replies: 2 speed up by a linear substitution of a quadratic polynomial ? Views: 850 Posted By bhelmes A peaceful night for you, The last program... A peaceful night for you, The last program was too slow. I am thinking of using the chinese remainder theorem in order to search for a factor of Mp. I would suggest a linear substitution for... 2021-09-15, 23:15 Replies: 2 speed up by a linear substitution of a quadratic polynomial ? Views: 850 Posted By bhelmes A peaceful and pleasant night for you, I... A peaceful and pleasant night for you, I have successfully implemented the following algorithm: 1. precalculate primes and n with help of f(n)=2n²-1 2. make a linear substitution with... 2021-09-09, 23:05 Replies: 2 speed up by a linear substitution of a quadratic polynomial ? Views: 850 Posted By bhelmes speed up by a linear substitution of a quadratic polynomial ? A peaceful and pleasant day for you, Let f(n)=2n²-1 and the linear substitution n=Mp*k+1, Mp is the exponent of the coresponding Mersenne number I know that there is a factor g | f(n0) if... 2021-09-04, 21:29 Replies: 21 factors of Mersenne numbers Views: 1,464 Posted By bhelmes The statement was not exactly formulated : ... The statement was not exactly formulated : if f>1 is the smallest factor of a Mersenne number, than there exists a n0>1 for the function f(n)=2n²-1 where n0 is the minimum, so that f | f(n0) and... 2021-09-03, 00:51 Replies: 21 factors of Mersenne numbers Views: 1,464 Posted By bhelmes factors of Mersenne numbers A peaceful and pleasant night for you, if f>1 is the smallest factor of a Mersenne number, than there exists a n0>1 for the function f(n)=2n²-1 where n0 is the minimum, so that f | f(n0) and...
 Forum: Dobri 2021-08-26, 20:14 Replies: 50 Incorrect guess based on limited data: Number of Primes 6k-1 > Number of Primes 6k+1 Views: 2,079 Posted By bhelmes Perhaps this is helpful for you: p 1 ... Perhaps this is helpful for you: p 1 3 5 mod 6 ------------------ 10 1 1 1 10^2 11 1 12 10^3 80 1 86 10^4 611 1 616 10^5 4784 1 ...
 Forum: Hardware 2021-08-10, 17:06 Replies: 23 Reducing electric power ? Views: 2,047 Posted By bhelmes A peaceful and pleasant day for you, I... A peaceful and pleasant day for you, I thought of adding a nvidia geforce 1030 card (passiv, 30 Watt) and use cudalucas instead of mprime. The cpu (Ryzan 3600) use ca. 110 Watt, and the computer... 2021-07-29, 20:09 Replies: 3 (p | ax²+bx+c) && (p | Ax²+Bx+C) Views: 534 Posted By bhelmes (p = a(x1)²+b(x1)+c) && (q = A(x1)²+B(x1)+C) @Dr Sardonicus It is always illuminating and friendly getting a response from you, thanks a lot for your clear and precious words. :hello: If p(x1)=a(x1)²+b(x1)+c and If q(x1)=A(x1)²+B(x1)+C... 2021-07-28, 00:51 Replies: 3 (p | ax²+bx+c) && (p | Ax²+Bx+C) Views: 534 Posted By bhelmes (p | ax²+bx+c) && (p | Ax²+Bx+C) A peaceful night for you, Let f(x)=ax²+bx+c and g(x)=Ax²+Bx+C with discriminant (f(x))=/=discr (g(x)) and f(x0)=g(x0) I am looking for a prime p>2 where p | f(x1) and p | g(x1) Is there a...
 Forum: Miscellaneous Math 2021-07-14, 23:29 Replies: 5 trial factoring for Mps Views: 1,003 Posted By bhelmes This was wrong, I have implemented this idea, but... This was wrong, I have implemented this idea, but the primes generating by the polynomial f(n)=2n²-1 do not "cover" completely the resulting quadratic polynomial. I think a sieve of Eratosthenes will... 2021-07-09, 20:32 Replies: 9 an²+bn+c = 0 mod p Views: 1,024 Posted By bhelmes @Nick, thanks a lot for your work and help. ... @Nick, thanks a lot for your work and help. an useful implementation in c and gmp of tonelli-shanks algorithm is: http://www.codecodex.com/wiki/Shanks-Tonelli_algorithm Let :... 2021-07-08, 21:18 Replies: 9 an²+bn+c = 0 mod p Views: 1,024 Posted By bhelmes Let an²+bn+c = 0 mod p If I want to... Let an²+bn+c = 0 mod p If I want to calculate the discriminant, can I first calculate a*=a mod p, b*=b mod p and c*=c mod p and then discr=(b*)²-4a*c* ? 2021-07-07, 02:56 Replies: 9 an²+bn+c = 0 mod p Views: 1,024 Posted By bhelmes I did not understand how to find the square of... I did not understand how to find the square of the discriminant b²-4ac mod 4an. b²-4ac is a quadratic residue, but not always a square. :loco: 2021-07-05, 19:24 Replies: 9 an²+bn+c = 0 mod p Views: 1,024 Posted By bhelmes an²+bn+c = 0 mod p Let f(n)=an²+bn+c = 0 mod p with n element of N and p prime. n=? Is there a better way than calculating f(n) for n=0 ...p-1 Thanks if you spend me some lines.
 Forum: Miscellaneous Math 2021-06-30, 00:14 Replies: 5 trial factoring for Mps Views: 1,003 Posted By bhelmes A peaceful night for you, I try to describe... A peaceful night for you, I try to describe a possible trial factor algorithm for mps: 0. Consider one mp. 1. Generate 10^9 primes and the n0 from the polynomial f(n)=2n²-1 2. Make a linear...
 Forum: Miscellaneous Math 2021-06-29, 01:21 Replies: 2 lineare substitution Views: 343 Posted By bhelmes A friendly good night for you Let f(n)=2n²-1... A friendly good night for you Let f(n)=2n²-1 and t|f(no) g(k)=2k²-1 - C where C is a constant for which k0 t|g(ko) ? this is not a linear substitution and I will be glad knowing the answer....
 Forum: Miscellaneous Math 2021-06-27, 18:31 Replies: 2 lineare substitution Views: 343 Posted By bhelmes Solving the linear substitution to k will do it. ... Solving the linear substitution to k will do it. :brian-e: :geek: :beer:
 Forum: Miscellaneous Math 2021-06-26, 23:00 Replies: 2 lineare substitution Views: 343 Posted By bhelmes lineare substitution A peaceful and pleasant night for you, Let f(n)=2n²-1 n=a+bk then f(a+bk)=2(a+bk)²-1= 2(a²+2abk+b²k²)=2a²+4abk+2b²k²=g(k) if t|f(n) for which k t|g(k) ? I am today a little bit stupid... 2021-06-20, 00:24 Replies: 10 how do I find a and b with a²+b²=1 mod f Views: 2,017 Posted By bhelmes A peaceful and pleasant night for you, For... A peaceful and pleasant night for you, For people who like php-scripts I added a calculator which decline from the pyth. trippel to the gaussian integer modulo f: ... 2021-06-11, 02:32 Replies: 10 how do I find a and b with a²+b²=1 mod f Views: 2,017 Posted By bhelmes Thanks a lot for all replies. :hello: Is... Thanks a lot for all replies. :hello: Is this a mathematical correct way: 1. Choose a,b with a>0 and b>0 and a=/=b and a²+b² =/=0 mod f (the trivial solutions are not important for me) 2.... 2021-06-10, 00:44 Replies: 10 how do I find a and b with a²+b²=1 mod f Views: 2,017 Posted By bhelmes how do I find a and b with a²+b²=1 mod f A peaceful and pleasant night for you, how do I find (fast ?) a gaussian number a+bi with a²+b²=1 mod f where f is an odd number. Perhaps this question might be interesting also for others. ...
 Forum: Miscellaneous Math 2021-06-07, 00:43 Replies: 0 was: a deterministic test for primes p=1 or p=7 mod 8 with 2 Selfridges Views: 192 Posted By bhelmes was: a deterministic test for primes p=1 or p=7 mod 8 with 2 Selfridges A peaceful and pleasant night for you, the counter example of the last test was wrong. There is a difference in the complex calculation: If you use a factor=gcd (a,b) from a+bi and define...
 Forum: Hardware 2021-06-06, 18:50 Replies: 23 Reducing electric power ? Views: 2,047 Posted By bhelmes I tried several possibilities in the Bios. All in... I tried several possibilities in the Bios. All in all there is not much progress. I think, I will run 200 DCs this year and switch off the computer in the hot season. Thanks for your replys. ...
 Forum: Miscellaneous Math 2021-06-02, 20:25 Replies: 10 rational points on the unit circle Views: 2,509 Posted By bhelmes You can visualize gaussian numers in two... You can visualize gaussian numers in two different ways: 1. Reducing it to the unit circle, so that the norm (a,b)=a²+b²= 1 mod p http://devalco.de/unit_circle/system_unit_circle.php?prim=127 ...
 Showing results 1 to 25 of 355

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