The filtered Frobenius eigenspaces of absolute prismatic cohomology offer p-adic Tate twists in mixed characteristic. They appear as the graded pieces of a motivic filtration on topological cyclic homology and in principle underly a general theory of p-adic étale motivic cohomology. Despite being “very far” from A^1-invariant, we will show how they can be used to define and study the p-adic part of A^1-invariant motivic cohomology, appearing as the graded pieces of Weibel’s homotopy invariant K-theory. This is a joint project with Tom Bachmann and Elden Elmanto, depending on previous work with Antieau, Bhatt, Clausen, Kelly, Lüders, Mathew, Nikolaus, and Scholze.