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Axial algebras of Jordan type $\eta$ are commutative algebras generated byidempotents whose adjoint operators have the minimal polynomial dividing$(x-1)x(x-\eta)$, where $\eta\not\in\{0,1\}$ is fixed, with restrictivemultiplication rules. These properties generalize the Pierce decompositions foridempotents in Jordan algebras, where $\frac{1}{2}$ is replaced with $\eta$. Inparticular, Jordan algebras generated by idempotents are axial algebras ofJordan type $\frac{1}{2}$. If $\eta\neq\frac{1}{2}$ then it is known that axialalgebras of Jordan type $\eta$ are factors of the so-called Matsuo algebrascorresponding to 3-transposition groups.  We call the generating idempotents {\it axes} and say that an axis is {\itprimitive} if its adjoint operator has 1-dimensional 1-eigenspace. It is knownthat a subalgebra generated by two primitive axes has dimension at most three.The 3-generated case has been opened so far. We prove that any axial algebra ofJordan type generated by three primitive axes has dimension at most nine. Ifthe dimension is nine and $\eta=\frac{1}{2}$ then we either show how to find aproper ideal in this algebra or prove that the algebra is isomorphic to certainJordan matrix algebras.

On primitive $3$-generated axial algebras of Jordan type