Here is the rub: Apple is so big, it’s running up against the law of large numbers.

Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger.

If Apple’s share price grew even 20 percent a year for the next decade, which is far below its current blistering pace, its $500 billion market capitalization would be more than $3 trillion by 2022. That is bigger than the 2011 gross domestic product of France or Brazil.

Put another way, to increase its revenue by 20 percent, Apple has to generate additional sales of more than $9 billion in its next fourth quarter. A company with $1 billion in sales has to come up with just another $200 million.

Robert Cihra, an analyst who covers Apple at Evercore Partners, told me this week that the law of large numbers as it applied to Apple had “been a concern for years now.” But, he said, “over the past couple of years, they have actually accelerated revenue growth. I don’t know that can continue indefinitely. If you extrapolate far enough out into the future, to sustain that growth Apple would have to sell an iPhone to every man, woman, child, animal and rock on the planet.”

The law of large numbers may explain why, even at its recent lofty stock price, Apple looks like a bargain by most measures. The ratio of its share price to its earnings, a common measure of a company’s stock value, is less than 11 based on earnings projections for this year. That is well below the market’s average P/E ratio of about 13. Apple shares are even being bought by so-called value investors, who are usually confined to stodgier, low-growth but arguably undervalued companies.