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Old 2021-06-07, 00:43   #1
bhelmes
 
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Mar 2016

22·32·11 Posts
Default 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 a:=a/factor and b:=b/factor then you do not remain in the same norm (a,b)=a²+b²=1 mod p
which was intended.

Furthermore the base a+bi should have also the norm (a,b)=-1 mod p

I think this is a good news

I repeat the test for p=7 mod 8


1) Choose a base a+bi with norm (a,b)=-1 mod p
2) for p = 7 mod 8 exp:=p+1
3) Calculate (a+bi)^(exp/4)=c+ci where gcd(c, p)=1 has to verify
If the gcd=/=1 p is not prime.
If the real part is equal the complex part then p is prime

Please have patience with me:
There might be some non known sideeffects of the vaccine
and the human brain might deliver some special effects.

Nevertheless I refer to mathematics arguments.

Last but not least you can see the calculation under
http://devalco.de/unit_circle/system...le.php?prim=31


Greetings from the unit circle
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