i have develloped a test for prime numbers mod 4 = 3.

It recognize all primes mod 4 = 3 below 10^9.

It uses complex numbers and needs only a fermat test.

If you are interested you will find it under

http://www.devalco.de/helmes_test.htm

I will try to generalize it.

Best greetings from the primes

Bernhard Helmes