Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Series of Primes

  1. Apr 22, 2007 #1
    Erdos noticed that [tex]\sum(-1)^n\frac{n\log n}{p_n}[/tex] diverges, where pn is the nth prime. I can't prove this conclusively. All I can say is that PNT implies that p_n~nlogn and thus the series "resembles" [tex]\sum(-1)^n[/tex].
  2. jcsd
  3. Apr 22, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If the terms don't go to zero, then the sum doesn't converge, right?
  4. Apr 22, 2007 #3
    Oh ya, how the hell did I miss that?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook