# Homework Help: Aren't there infinitely many primes?

1. Aug 2, 2015

### PcumP_Ravenclaw

1. The problem statement, all variables and given/known data
sn= 1/n if n is a prime number; sn = 0 if n is not prime.

2. Relevant equations

3. The attempt at a solution
We know that there are infinitely many prime numbers as n tends to infinity so why is $\frac{1}{(prime number)}$ not equal to zero when n is a prime number?

2. Aug 2, 2015

### SammyS

Staff Emeritus
It looks like Sn is a term in a series with a particular definition. That definition is what you have given.

Is this a fragment from a problem you have been given.

3. Aug 3, 2015

### PcumP_Ravenclaw

The question to this problem is as below.

For each of the sequences defined in below, state whether or not it tends
to a limit. If a sequence has a limit, make an $(\epsilon,N )$ table, taking
$\epsilon = 0.001$ and any other values that you like.

4. Aug 3, 2015

### Ray Vickson

When n is an integer (prime or not), 1/n is not zero; however, it is small if n is large. In fact, 1/n is never 0, but $0 = \lim_{n \to \infty} 1/n$.

5. Aug 3, 2015

### HallsofIvy

Because there are an infinite number of primes, the limit as n goes to infinity of your sequence is 0. Now, $\frac{1}{primenumber}$ is a different sequence all though its limit is also 0.

Your series "$a_n$" is 0, 1/2, 1/3, 0, 1/5, 0, 1/7, 0, 0, 0, 1/11, ...
Your series "$\frac{1}{primenumber}$" is 1/2, 1/3 ,1/5, 1/7, 1/11, 1/13, 1/17, ...

6. Aug 4, 2015

### PcumP_Ravenclaw

how do you know that for the an sequence non-prime terms for n equal 0? its not given in the question.

7. Aug 4, 2015

### SammyS

Staff Emeritus
It is given in the definition of the sequence.

It seems you don't understand the word "defined".

The definition of this sequence is:

sn = 1/n, if n is prime
sn = 0, if n is not prime​

1 is not prime, so s1 = 0
2 is prime, so s2 = 1/2
3 is prime, so s3 = 1/3
4 is not prime, so s4 = 0
5 is prime, so s5 = 1/5
6 is not prime, so s6 = 0
7 is prime, so s7 = 1/7
8 is not prime, so s8 = 0
9 is not prime, so s9 = 0
10 is not prime, so s10 = 0
11 is prime, so s11 = 1/11
...

Get it ?

8. Aug 4, 2015

### PcumP_Ravenclaw

yes right. Its given in the question. danke!! Haste leads to waste!!