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The information in this preliminary prospectus is not complete and may be changed. This preliminary prospectus supplementand the accompanying prospectus are not an offer to sell these securities and are not soliciting an offer to buy these securitiesin any jurisdiction where the offer and sale is not permitted. Subject to Completion, dated January 23, 2026 PRELIMINARY PROSPECTUS SUPPLEMENT(to Prospectus dated January 20, 2026) Daxor Corporation Shares of Common Stock Daxor Corporation is an investment company with medical instrumentation and biotechnology operations. While the company is notprimarily engaged in the business of investing, reinvesting, owning, holding or trading in securities, the company is dependent uponearnings from its investment portfolio to fund operations and has registered as a closed-end investment company under the InvestmentCompany Act of 1940, as amended (the “Investment Company Act”).While Daxor Corporation is registered as a closed-endinvestment company, it has always conducted its business as an operating company and has never been in, or held itself out to be in,the business of investing, reinvesting, owning, holding or trading in securities. We intend to file an application pursuant to Section 8(f) of the Investment Company Act seeking an order declaring that Daxor hasceased to be a registered investment company. Investors in registered investment companies benefit from legal protections imposed fortheir benefit under theInvestment Company Act, and those legal protections will no longer apply if we receive the requested order. The company is offeringshares of our common stock, par value $0.01 per share (referred to as “Common Stock”) in aregistered direct offering, at a purchase price of $per share of Common Stock pursuant to this Prospectus Supplement and theaccompanying Prospectus. During any 12-month period, the aggregate market value of securities we may offer under this registration statement shall not exceedone third of the aggregate market value of voting and non-voting common equity held by persons who are not affiliates of ourcompany, and this maximum amount is currently $10,866,275.60, based on the last reported sale price of $14.75 on December 31,2025, which would currently limit aggregate offerings to approximately 806,701 shares of Common Stock, assuming all shares aresold at $13.47 per share, the closing price on January 20, 2026. In no event will we sell our Common Stock in a primary offering underthis registration statement with a value exceeding one-third of our public float in any 12-month period. We have not offered anysecurities pursuant to the SEC rules noted above during the 12 calendar months prior to and including the date of this prospectussupplement. We have engaged Lake Street Capital Markets, LLC, or the placement agent, as our exclusive placement agent in connection with thisoffering. The placement agent has no obligation to buy any of the securities from us or to arrange for the purchase or sale of anyspecific number or dollar amount of securities. We have agreed to pay the placement agent the placement agent fees set forth in thetable below. See “Plan of Distribution” beginning on page S-8 of this Prospectus Supplement for more information regarding thearrangements with the placement agent. (1)We have agreed to reimburse the placement agent for certain expenses in connection with this offering. See “Plan ofDistribution” for additional information regarding total placement agent. Delivery of the shares of common stock offered hereby is expected to occur on or about , 2026. Investing in the Common Stock involves certain risks. See “Risk Factors” beginning on page S-2 herein and the “Risk Factors”beginning on page 11 of the accompanying Prospectus. You should consider carefully these risks together with all of the otherinformation contained in this Prospectus Supplement and the accompanying Prospectus before making a decision to purchaseCommon Stock. Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of thesesecurities or determined if this Prospectus Supplement or the accompanying Prospectus is truthful or complete. Anyrepresentation to the contrary is a criminal offense. Lake Street This Prospectus Supplement is dated, 2026. As of, 2026, the last reported sale price for the Common Stock on the Nasdaq Capital Market was $per share. The netasset value (“NAV”) per share of the Common Stock as of the close of business on, 2026was $, representing a premiumof market price to NAV of%. Our currently outstanding shares of Common Stock are, and the shares of Common Stock offered by this Prospectus Supplement andthe accompanying Prospectus will be, listed on the Nasdaq Capital Market under the symbol “DXR”. This Prospectus Supplement, together with the accompanying Prospectus, dated January 20, 2026, sets forth the information that youshould know before investing in shares of Comm