TITLE: Are $E_n$-operads not formal in characteristic not equal to zero?
QUESTION [11 upvotes]: This is a short question:
Is it just unproven folklore (yet), or is it definitively known that $E_n$-operads are not formal, if the characteristic of the underlying field is not equal to zero?

REPLY [3 votes]: Paolo Salvatore put a paper on the arXiv last week (1807.11671) proving that $E_2$ is not formal over $\mathbb{F}_2$ as a non-symmetric operad (what he calls planar operad), i.e. you cannot find a zigzag of quasi-isomorphisms of operads (not necessarily $\Sigma$-equivariant) between $H_*(E_2; \mathbb{F}_2)$ and $C_*(E_2; \mathbb{F}_2)$. He uses obstruction theory for that.