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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


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    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?
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