mersenneforum.org a d̶e̶t̶e̶r̶m̶i̶n̶i̶s̶t̶i̶c̶ test for primes p=1 or p=7 mod 8 with 2 (??) Selfridges
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2021-04-03, 23:27   #1
bhelmes

Mar 2016

22·34 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.

Attached Files
 deterministic_algorithm_helmes.pdf (26.7 KB, 25 views)

 2021-04-03, 23:47 #2 paulunderwood     Sep 2002 Database er0rr 7×523 Posts Please give us a worked example for the prime 97.
2021-04-04, 00:18   #3
bhelmes

Mar 2016

22×34 Posts

Quote:
 Originally Posted by paulunderwood Please give us a worked example for the prime 97.
http://devalco.de/unit_circle/system...le.php?prim=97

This seems to be ok.

2021-04-04, 12:57   #5
Dr Sardonicus

Feb 2017
Nowhere

4,519 Posts

Quote:
 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?
Quote:
 2. Calculate the exponent a) f=1 mod 8 exp:=(p-1)/4 b) f=7 mod 8 exp:=(p+1)/4
What is p? It is not previously defined.

Giving up...

 2021-04-04, 13:41 #6 bhelmes     Mar 2016 14416 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:=(p-1)/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:=(f-1)/4 b) f=7 mod 8 exp:=(f+1)/4
2021-04-04, 14:23   #7
Dr Sardonicus

Feb 2017
Nowhere

4,519 Posts

Quote:
Originally Posted by bhelmes
Quote:
 Originally Posted by Dr Sardonicus "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)
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.
Quote:
 Originally Posted by Dr Sardonicus What is p? It is not previously defined.
Quote:
 This was a "thinking error" or in german a "Denkfehler" a) f=1 mod 8 exp:=(f-1)/4 b) f=7 mod 8 exp:=(f+1)/4

 2021-04-04, 14:44 #8 bhelmes     Mar 2016 22·34 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.
 2021-04-05, 04:07 #9 bhelmes     Mar 2016 22·34 Posts I think you have to add one condition: 1. b) (a+bi)^(exp/8)=/=1+i mod f
 2021-04-05, 04:59 #10 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23·11·107 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: Process A. (aka 3.) Calculate and verify that (a+bi)^exp = 1+i mod f Process B. Calculate and verify that a^exp = 1 mod fIs it true that these processes require the same time? You seem to assume that to be true.
 2021-04-06, 11:57 #11 bhelmes     Mar 2016 5048 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 ? Covid-19- time is quite boring but perhaps the situation will become better. Have a pleasant time, Bernhard

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