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.