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et's take an example. Suppose you want to know how many primes there are less than one trillion (that's 1012). To use method A), we need to know what ln(1012) is. Well, that's obviously 12 times ln(10), and ln(10) is a number you may want to memorize (an approximation for) if you care about prime counting. It's about 2.30. So 12 times this is about 27.6, and therefore the number of primes up to a trillion is about a trillion divided by 27. In other words: roughly 1 number out of 27 in this range is a prime. That's actually a pretty useful way to understand the answer - much more intuitive than the precise number of such primes (which, incidentally, is 37,607,912,018).