Exactly as Hamilton has pointed it out.
What has not yet be mentioned is that all operations are performed in the factor ring Z/nZ with n being the prime modulus of the secp256k1 curve.
Example: if n was 7 (which it isn't) then 4*4 = 16 mod 7 == 2
The modulo operations were clear for me.
I just needed a formula for point multiplication G by the private key.
Now I understand my error.
I haven't checked it yet, but I will try to calculate the public key manually and compare it with bitaddress.org