let p be a rational prime,K a number field. Dedekind's discriminant theorem tells us: p ramifies in K <==> p divides discriminant of K. hence if p does not divide discriminant of K, (p) will either splits,i.e.(p)=P_1P_2 (P1=/= P2) or (p) remains prime. now,my question is : there are some criterias which can tell if p will split or remain prime.