1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Aren't there infinitely many primes?

  1. Aug 2, 2015 #1
    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. jcsd
  3. Aug 2, 2015 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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.

    Please state the complete problem.
     
  4. Aug 3, 2015 #3
    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.
     
  5. Aug 3, 2015 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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 ##.
     
  6. Aug 3, 2015 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

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

    Your series "[itex]a_n[/itex]" is 0, 1/2, 1/3, 0, 1/5, 0, 1/7, 0, 0, 0, 1/11, ...
    Your series "[itex]\frac{1}{primenumber}[/itex]" is 1/2, 1/3 ,1/5, 1/7, 1/11, 1/13, 1/17, ...
     
  7. Aug 4, 2015 #6
    how do you know that for the an sequence non-prime terms for n equal 0? its not given in the question.
     
  8. Aug 4, 2015 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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 ?
     
  9. Aug 4, 2015 #8
    yes right. Its given in the question. danke!! Haste leads to waste!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted