2021-06-07, 00:43 | #1 |
Mar 2016
2^{2}·3^{2}·11 Posts |
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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