There are plenty of reports today that Apple is now officially the most valuable company in history. However, there are at least three other claimants to the crown, depending on the methodology.

The claims are based on market capitalization, which is the number of shares in a company that could conceivably be bought and sold on the open market, multiplied by the current market price. It’s one “on paper” measure of a company’s value and theoretically if you had that much money, you could buy the company. (In practice, launching a total takeover bid would likely drive the price up.)

As Apple’s stock price continues to rise, its market cap has previously attracted headlines, first when it overtook Microsoft, and then when it overtook Exxon Mobil to become number one on US stock markets.

This week’s excitement came when Apple’s market capitalization topped $618.9 billion. That was the figure hit by Microsoft in 1999 that, until now, was an all-time record.

Several sources are already questioning the idea that Apple is now the all-time number one. One argument, championed by the Columbia Journalism Review in a criticism of press coverage of the figure, is that because market capitalization is effectively a fictional figure, it’s completely unfair and meaningless not to take inflation into account when making “all time” comparisons. It notes that Microsoft’s 1999 figure is worth $854.3 billion in today’s money.

However, Microsoft circa 1999 isn’t necessarily the record holder either. To find the true all-time champ, you’d need to look at every company that’s ever been number one and crunch the figures. Nobody (including me) seems to have much inclination to do that, though Tech Digest figures the strongest candidate is another tech firm: it notes that the IBM of 1967 had a market cap of $192.3 billion, which translates at a whopping $1.3 trillion today.

It may also be that all of these figures have to be qualified as merely the biggest in the tech industry or in the United States. PetroChina technically beat the one trillion dollar mark when its stock briefly doubled in price on its first day of trading. That was a misleading figure however as it was based on the number of shares across all markets, but only on the price on the Shanghai exchange.