20210403, 23:27  #1 
Mar 2016
2^{2}·3^{2}·11 Posts 
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 „mapped“ on the unit circle for the different angles. As every rational point on the unit circle has 8 „combined“ rational points (tangens = cotagans and mirrored in the four quaters), you can count the rational points. If the amount of the rational points are equal to the complex order in the unit circle of f, f is sure to be prime. This is a discussion paper in the attachment, if you find an error, regard it as easter egg. 
20210403, 23:47  #2 
Sep 2002
Database er0rr
2·29·71 Posts 
Please give us a worked example for the prime 97.

20210404, 00:18  #3 
Mar 2016
2^{2}·3^{2}·11 Posts 

20210404, 07:15  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
7×23×61 Posts 
What is 'deterministic' about this test?

20210404, 12:57  #5  
Feb 2017
Nowhere
2×3×31^{2} Posts 
Quote:
Quote:
Giving up... 

20210404, 13:41  #6 
Mar 2016
2^{2}·3^{2}·11 Posts 
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" how, exactly? These are the red elements in the graphic: http://devalco.de/unit_circle/system_unit_circle.php (I think this is a wonderful applet, programmed in php) 2. Calculate the exponent a) f=1 mod 8 exp:=(p1)/4 b) f=7 mod 8 exp:=(p+1)/4 > What is p? It is not previously defined. This was a "thinking error" or in german a "Denkfehler" a) f=1 mod 8 exp:=(f1)/4 b) f=7 mod 8 exp:=(f+1)/4 
20210404, 14:23  #7  
Feb 2017
Nowhere
5766_{10} Posts 
Quote:
Quote:


20210404, 14:44  #8 
Mar 2016
2^{2}×3^{2}×11 Posts 
> 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 residue with the described conditions, but unfortunetly this is not true: 4+7i is not a good candidate for http://devalco.de/unit_circle/system...le.php?prim=89. I called my paper a discussion paper, therefore perhaps someone has some better ideas. The algorithm should not be a probablistic test for primes, therefore I thought "deterministic " should be the right term. 
20210405, 04:07  #9 
Mar 2016
2^{2}×3^{2}×11 Posts 
I think you have to add one condition:
1. b) (a+bi)^(exp/8)=/=1+i mod f 
20210405, 04:59  #10 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23135_{8} Posts 
Let's make a short test that will help us define the runtime of this test (as if it worked, though no data is presented that it does).
Here is the question: Compare two short processes:Is it true that these processes require the same time? You seem to assume that to be true. 
20210406, 11:57  #11 
Mar 2016
2^{2}×3^{2}×11 Posts 
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 mathematical world when the paper "Primes in P" appeared, why not follow this thread ? Covid19 time is quite boring but perhaps the situation will become better. Have a pleasant time, Bernhard 
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