  We provide an explicit description of the primitive ideals of the enveloping
algebra $\operatorname{U}(\frak{sl}(\infty))$ of the infinite-dimensional
finitary Lie algebra $\frak{sl}(\infty)$ over an uncountable algebraically
closed field of characteristic 0. Our main new result is that any primitive
ideal of $\operatorname{U}(\frak{sl}(\infty))$ is integrable. A classification
of integrable primitive ideals of $\operatorname{U}(\frak{sl}(\infty))$ has
been known previously, and relies on the pioneering work of A. Zhilinskii.
