Gaussian Primes

[sven-h.simon]

Hallo,

after our discussions about Gaussian Primes I contributed a new sequence to 
OEIS. The elements are the Gaussian Primes in the first quadrant of the complex 
plane, numbers a+bi, having a>0, b>=0. In the sequence the primes are ordered by 
their norm, and if two primes have the same norm, by the size of the real part 
of the number.

The sequence starts 
1+i,1+2i,2+i,3,2+3i,3+2i,1+4i,4+i,5,2+5i,5+2i,1+6i,6+i,4+5i,5+4i,7,2+7i,7+2i,...

With an additional unit (-1, i or -i), every complex number can be completly 
factored into the primes of this sequence. No prime of the sequence can be 
factored into an other prime of the sequence and a unit, there are no associated 
numbers in the sequence.

The real part is in sequence A103431, the imaginary one in A103432.

Sven