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I've just begun the "Concrete Mathematics" book by Knuth et al. In the first section about sums (and I apologise if this is really trivial, but I'm new and struggling a little); and they show this as one of the examples:

$\sum_{k = 1}^{\pi(N)} \frac{1}{p_{k}}$

"This is the sum of all reciprocals of prime numbers between 1 and N."

If you didn't have the explanation here, how would you know that N is supposed to be a prime number? Is it because of the pi symbol? Also, does pi often represent a number as prime?

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Not that it's relevant to this question, but in fact in Algebraic Number Theory one often uses $\pi$ to stand for a prime number. –  Gerry Myerson Aug 27 '12 at 5:48
    
@GerryMyerson Nono, I appreciate your time, and in fact I was stressing over some phantom relationship between the number $\pi$ and the symbol used in this case. So that does help! –  yoonsi Aug 27 '12 at 5:50

2 Answers 2

up vote 6 down vote accepted

$\pi(N)$ is the prime-counting function, i.e. the number of primes not exceeding $N$.

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Both useful answers but I'm going to choose this as my correct answer because the further reading provided helped me a lot. Thank you both! –  yoonsi Aug 27 '12 at 5:51

$N$ is not supposed to be a prime number. $\pi(N)$ denotes the number of primes $\leq N$ and is (obviously) a function of $N$. Similarly, $p_k$ is the $k$th prime .

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