Apple is now the most valuable company of all time.

Shares are rising again, continuing the sharp run-up of the past few weeks that has propelled the tech juggernaut to its all-time high.

The stock recently rose 1.8% at $660, pushing Apple’s market capitalization up to $619 billion, FactSet data show. The previous historical record for top market cap belonged to Microsoft, whose market value topped out at $616.3 billion in December 1999, according to Howard Silverblatt, senior index analyst at S&P Dow Jones Indices.

Now Apple holds the distinction as the most valuable company by market capitalization.

Apple’s market cap is also more than $200 billion greater than Exxon Mobil – the second biggest company right now clocking in at $405 billion. Microsoft, Wal-Mart and IBM round out the top five.

Rumors of new iPhone and iPad products have been running rampant of late, helping to give shares their latest boost. Many analysts anticipate an iPhone 5 launch is coming in September.

Last week, Jefferies boosted its price target on Apple to $900. Earlier this year, two firms slapped $1,000 price targets on the company, while predicting Apple’s market cap will top $1 trillion. (Our friends at All Things D point out the stock price would have to hit about $1072 for Apple to become the world’s first trillion-dollar company).

Apple’s sway on major benchmark indexes has been well documented for much of the year. But the latest figures from Silverblatt underscore just how important Apple’s rally is for the rest of the market.

The S&P 500′s tech sector is up 16% since October 2007 when the broad market hit its all-time peak, he says. But stripping away Apple from the calculation and the sector is down 3.7% throughout that same time frame.

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