## Empty one year ago Does this infinite series have a closed form?

1. Empty

$\sum_{i=1}^{\infty} \frac{1}{p_i^{p_i}}$ Where $$p_i$$ is the ith prime.

2. Empty

It appears to approach this since the terms die off really quickly: $S \approx 0.287358...$ Does that resemble anything you've seen before? All I can say is it's slightly larger than e/10. Hahaha. http://www.wolframalpha.com/input/?i=1%2F2%5E2%2B1%2F3%5E3%2B1%2F5%5E5%2B...&t=crmtb01

3. Empty

Turns out base e and base 10 are more related than we thought? Ok probably not haha.

4. ganeshie8
5. ganeshie8

looks there isn't much online on this series

6. anonymous