In the search for the exact minimum of the tachyon potential in the Witten's cubic string field theory we try to learn as much as possible from the string field theory in the large B-field background. We offer a simple alternative proof of the Witten's factorization, carry out the analysis of string field equations also for the non-commutative torus and find some novel relations to the algebraic K-theory. We note an intriguing relation between Chern-Simons and Chern classes of two non-commutative bundles. Finally we observe a certain pattern which enables us to make a plausible conjecture about the exact form of the minimum.