The 346,000 number is based on some old and obsolete information about Rock Island production. The last verified Rock Island serial number was 430,742.
As p246 said, a relatively large number of Rock Island receivers and other parts was sent to Springfield in the mid-1920s. John Beard has stated that from about s/n 375,000-405,000, about 50% were used with Springfield parts; from about 405,000 until 430,742, the percentage used was significantly highly, I believe John said 75-85%.
I'm assuming the rest were used to assemble complete Rock Island rifles, or kept as spare parts at RIA. John can probably correct or clarify what I said.
"We make men without chests and expect from them virtue and enterprise. We laugh at honor and are shocked to find traitors in our midst."
--C.S. Lewis