is the number of primes less than x. , then, is the proportion of integers less than x that are primes.b) This one I'm not sure about, and there's no answer in my text. My guess is that it's the number of primes per integer, but that could be my ignorance talking.
The mean value theorem says that (f(b)- f(a))/(b- a)= f'(c) for some number c, between a and b. Applying that to the function Li(x) on the interval says that for some c between 2 and . Of course, Li(2)= 0 and I suspect you can approximate by without significant error. So you are saying that for some c less than . It is, of course, easy to find Li'(x). How large does that get to be?There's more parts to this question, but I'm going to see if I can attempt them first. Meanwhile, is what I've done the correct approach? Thanks.
Ok, this is the other question I need assistance with:
d) By applying the Mean Value Theorem to Li on the interval , find a lower bound for