1+Sum of primes^-1 * (-1)^(PI)

[Matt Benesi]

Is this series divergent and what is its name? If the series is not divergent, what is the constant named? Note that $\pi$ is the prime counting function, or number of primes.

$$1+\sum_{p=primes}^{\infty}\frac{(-1)^{\pi}}{p}={1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{5}+\frac{1}{7}-\frac{1}{11}...$$

Thanks :D

 

[mathman]

http://mathworld.wolfram.com/PrimeSums.html

Above has this series.

 

[Matt Benesi]

Thanks.