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Forum: Miscellaneous Math 2021-04-09, 17:31
Replies: 35
Views: 690
Posted By bhelmes
What about an adding pretest like q^((f-1)/2)=f-1...

What about an adding pretest like q^((f-1)/2)=f-1 mod f.
This costs only one Selfridge and should exclude the counterexamples.





Thanks a lot of your amazing work, I get a bit jealous of...
Forum: Miscellaneous Math 2021-04-08, 23:32
Replies: 35
Views: 690
Posted By bhelmes
13361 is the smallest counterexample for this...

13361 is the smallest counterexample for this test.
http://devalco.de/unit_circle/system_unit_circle.php?prim=13361
1+10i was the base. :redface: :unsure: :loco:
Forum: Miscellaneous Math 2021-04-07, 15:11
Replies: 35
Views: 690
Posted By bhelmes
The last program version had some errors, which I...

The last program version had some errors, which I fixed in the new attached version. You have to substitute .c with .php

I think the program is easy to understand.

I run up to 8000 and there...
Forum: Miscellaneous Math 2021-04-06, 23:57
Replies: 35
Views: 690
Posted By bhelmes
A peaceful and pleasant night for you, Batalov ...

A peaceful and pleasant night for you, Batalov

First changing the title of this thread and then asking ?

Nevertheless I gave a mathematical explication and some arguments just some messages...
Forum: Miscellaneous Math 2021-04-06, 14:48
Replies: 35
Views: 690
Posted By bhelmes
I can offer (soon) a program in C or php, a...

I can offer (soon) a program in C or php, a (fast) exponention with complex numbers is needed, with some regards to symmetrics in addition and that is all.


I did not get familar with Pari/GP.
...
Forum: Miscellaneous Math 2021-04-06, 13:35
Replies: 35
Views: 690
Posted By bhelmes
My description is not perfect, I know, therefore...

My description is not perfect, I know, therefore I called it "discussion paper",
On the indicated website there is a sentence which explains it, and I tried to emphasize that I am regarding the...
Forum: Miscellaneous Math 2021-04-06, 13:15
Replies: 35
Views: 690
Posted By bhelmes
tan (alpha)=a/b=4/4=1/1 better ?

tan (alpha)=a/b=4/4=1/1 better ?
Forum: Miscellaneous Math 2021-04-06, 12:58
Replies: 35
Views: 690
Posted By bhelmes
I use some symmetric calculation: -3 = 4 mod 7...

I use some symmetric calculation:
-3 = 4 mod 7 therefore:
(1+2i)² = -3 +4i = 4+4i = 1+i (mod 7)


I regard the tangens (alpha)= a/b
if res:=gcd (a, b)>1 I replace it by a:=a/res; b:=b/res;

...
Forum: Miscellaneous Math 2021-04-06, 12:49
Replies: 35
Views: 690
Posted By bhelmes
A peaceful day for you, I will give a short...

A peaceful day for you,

I will give a short explication, why I think, that the test is deterministic:

I regard an angle resp. a+bi with the described proporties,
if I make an addition of the...
Forum: Miscellaneous Math 2021-04-06, 11:57
Replies: 35
Views: 690
Posted By bhelmes
A peaceful day for you, Batalov it would be...

A peaceful day for you, Batalov

it would be gentle from you to give a counterexample for the test
before you delete the "deterministic" word in the title.

There was a lot of joy in the...
Forum: Miscellaneous Math 2021-04-05, 04:07
Replies: 35
Views: 690
Posted By bhelmes
I think you have to add one condition: 1. b)...

I think you have to add one condition:
1. b) (a+bi)^(exp/8)=/=1+i mod f


:brian-e: :geek: :redface: :rolleyes:
Forum: Miscellaneous Math 2021-04-04, 14:44
Replies: 35
Views: 690
Posted By bhelmes
> No algorithm is given, and the applet is...

> No algorithm is given, and the applet is restricted to odd numbers less than 1000. I can factor odd numbers less than 1000 in my head.


I thought that you could use every non quadratic...
Forum: Miscellaneous Math 2021-04-04, 13:41
Replies: 35
Views: 690
Posted By bhelmes
1. Choose a complex gaussian number a+bi ...

1. Choose a complex gaussian number a+bi

with the norm a2+b2 < f and
with gcd (a,b)=1,
with gcd (b, f)=1 and
jacobi (a2+b2, f)=-1 (the norm should be a non quadratic residue)

>"Choose"...
Forum: Miscellaneous Math 2021-04-04, 00:18
Replies: 35
Views: 690
Posted By bhelmes
http://devalco.de/unit_circle/system_unit_circle.p...

http://devalco.de/unit_circle/system_unit_circle.php?prim=97


This seems to be ok.
Forum: Miscellaneous Math 2021-04-03, 23:27
Replies: 35
Views: 690
Posted By bhelmes
a d̶e̶t̶e̶r̶m̶i̶n̶i̶s̶t̶i̶c̶ test for primes p=1 or p=7 mod 8 with 2 (??) Selfridges

Pleasant easter days,

I present a new prime algorithm:

I consider the order in the complex field reduced to the unit circle and count the rational numbers which can be...
Forum: Hardware 2021-03-23, 18:49
Replies: 1
Views: 126
Posted By bhelmes
huge of the 3.level cache for optimal testing Mp

A peaceful day,

I have an amd cpu with 32MB 3. level cache and make double checking.

Is the 3. level cache big enough for first prime checking resp.
how much space does the implemented fft...
Forum: Number Theory Discussion Group 2021-03-17, 21:13
Replies: 15
Views: 1,322
Posted By bhelmes
Oh, I think I have made an error in the...

Oh, I think I have made an error in the programming part, sorry for that.


Covid-19 is not good for my health and takes too long.


I think I will make a small holiday time. Computer is...
Forum: Number Theory Discussion Group 2021-03-16, 21:21
Replies: 15
Views: 1,322
Posted By bhelmes
Somebody wanted to know how the sieving for...

Somebody wanted to know how the sieving for quadratic polynomials is made. I recommand to this topic my (nice) webpage:
http://devalco.de/#106


or my book to this topic:...
Forum: Combinatorics & Combinatorial Number Theory 2021-02-23, 14:32
Replies: 9
Views: 13,290
Posted By bhelmes
A peaceful and pleasant day in spite of Covid-19 ...

A peaceful and pleasant day in spite of Covid-19



I noticed that the factors of Mp-1 have the following proporty:
r odd and r | p-1 then the factors f of Mp-1 with f > p are f=1 mod r

I...
Forum: Number Theory Discussion Group 2021-02-09, 01:16
Replies: 9
Views: 3,142
Posted By bhelmes
Thanks for the function.

Thanks for the function.
Forum: Number Theory Discussion Group 2021-02-07, 18:15
Replies: 9
Views: 3,142
Posted By bhelmes
Does someone has a function in gmp for...

Does someone has a function in gmp for calculating mpz_mod_mp ?


Would be nice for me and perhaps also for others.


Greetings :cmd: :tom: :whistle:

Bernhard
Forum: Number Theory Discussion Group 2021-02-05, 23:58
Replies: 15
Views: 1,322
Posted By bhelmes
Mp67 less than a second M1 A :71 B :6...

Mp67 less than a second


M1
A :71
B :6
C :6
D :1
Forum: Number Theory Discussion Group 2021-02-05, 22:04
Replies: 15
Views: 1,322
Posted By bhelmes
Example : f=14111 M = (A B) (C D) ...

Example : f=14111

M =
(A B)
(C D)

The matrix M is calculated by fast exponention with primes from 2 up to max modulo f

basis polynom : 2x²-1
(I calculate the primes p | 2x²-1 with...
Forum: Number Theory Discussion Group 2021-01-31, 17:06
Replies: 15
Views: 1,322
Posted By bhelmes
a factorisation algorithm with help of quadratic polynomials

A peaceful and pleasant sunday for you,


I present a new factorisation algorithm, which use quadratic polynomials instead of eliptic curves.


It is a preprint and an implementation will...
Forum: Miscellaneous Math 2021-01-28, 21:28
Replies: 40
Views: 1,840
Posted By bhelmes
primesieves for quadratic polynomials: ...

primesieves for quadratic polynomials:
http://devalco.de/#106
Showing results 1 to 25 of 322

 
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