The e-mail you get after you write an article about number theory is very interesting. For one thing, you’re reminded of phrasings which have one meaning among mathematicians, but a slightly different one outside the tribe.
The majority of the e-mail I’ve gotten about the bounded gaps piece concerns two questions of this kind: I’ll answer them both here, in case other readers are following the link from Slate to the blog.
Q: You say that the number of primes less than X is about X/log(X), but don’t you mean X/ln(X)?
A: When mathematicians say “log” we mean the natural log, the thing which in some other contexts (e.g. Google’s search bar calculator) is denoted “ln.” But mathematicians never say “ln.” (To be honest, we kind of think the base-10 logarithm should be called “lu.”)
Q: You say that every positive number is the product of primes, but this is not true for prime numbers themselves, which can’t be expressed as products.
A: A prime number is indeed the product of prime numbers! It is the product of just one prime number, itself.
What about 1? It’s the product of zero prime numbers.