I don't have much detailed information about logo vs. no logo guns in my database, but the highest SN on my list of an M&P without a logo is 336927. Undated, but it probably shipped in April or May 1920 based just on that SN. The SN of the earliest post-WWI M&P I list as having a logo is 360812, also undated. So somewhere between must be the logo re-start, possibly in the 34xxxx-35xxxx SN range. Perhaps someone else can narrow the gap.