Anthropic's IPO is expected to come roughly five months after Elon Musk took SpaceX public in a record offering. AI company Anthropic plans to offer 825 million shares in Nasdaq listing; IPO could raise up to $64.35 billion. The Anthropic IPO is shaping up to be one of the stock market debuts in history when it lists on Nasdaq, with major companies and investors also committing billions to the offering.