The record valuation, which defied sceptics' predictions that the stock price would wallow, cheered Crown Prince Mohammed bin Salman, who had championed the public offering.
Saudi Aramco has finally set an initial public offering date in December while the country's Capital Market Authority has placed a number of conditions to reduce risk.
As Putin makes his second visit to Riyadh in 12 years, Saudi-Russia relations remain steady, despite the countries being on different sides of several thorny geopolitical issues.
The attacks on Saudi Arabia, the world's largest oil producer, show there are circumstances under which an energy-dominant country can lose its supposed dominance fast.