# Series of Primes

1. Apr 22, 2007

### Dragonfall

Erdos noticed that $$\sum(-1)^n\frac{n\log n}{p_n}$$ 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" $$\sum(-1)^n$$.

2. Apr 22, 2007

### Hurkyl

Staff Emeritus
If the terms don't go to zero, then the sum doesn't converge, right?

3. Apr 22, 2007

### Dragonfall

Oh ya, how the hell did I miss that?