Is there a generalization of Goldbachs conjecture for prime ideals in number fields?
Googling the obvious, «Goldbach number fields», comes up with a bunch of relevant results, In particular, a link to [Takayoshi MITSUI, On the Goldbach problem in an algebraic number field I. J. Math. Soc. Japan, Vol 12, No. 3, 1960] here 

