# Series of Primes

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" $$\sum(-1)^n$$.

Related Linear and Abstract Algebra News on Phys.org
Hurkyl
Staff Emeritus