Axial algebras of Monster type (α,β) are a class of non- associative algebras that includes, besides associative algebras, other important examples such as the Jordan algebras and the Griess algebra. 2-generated primitive axial algebras of Monster type (α,β) naturally split into three cases: the case when α ∈/ {2β, 4β}, the case α = 4β and α = 2β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).
