So a while back I was on the internet and had encountered a website containing an experimental search for identities for $\pi$. My memory was that the page belonged to either Jonathan Sondow or Michael Somos, but now I am not sure (I don't even know if I trust my memory on the 'S' in the last name) . The page most likely belongs to Jim Cullen and I have been wrongly attributing the open status of these identities to Gourevitch's conjecture (special thanks to Timothy Chow for reverse-engineering my brain and revealing this very unfortunate mental hash collision).

Basically they had experimentally searched the space of identities of the form $\sum_{n=0}^{\infty} \frac{1}{P(n)}$ over a large number of polynomials $P(n)$ and used a tool like Munafo's RIES to see if they matched any known forms. They had struck gold finding some unusual identities involving either $\pi^2$ or $\pi^4$ with quadratic or quartic denominators (I don't remember which). These identities looked like they should be related to the riemann zeta function but the identities had no known proof/explanation at the time.

1. find this website so at least I can edit this question and give the person due credit.

2. Ask what the state of those identities are. Do they remain open?

I am very happy with the answers and comments this question has generated. I think other people interested in $\pi$ formulas will probably find this as a useful exploration point.

I assume Gourevitch's Conjecture remains open although if anyone had updates on it they could post here or this more trafficked location

So a while back I was on the internet and had encountered a website containing an experimental search for identities for $\pi$. My memory was that the page belonged to either Jonathan Sondow or Michael Somos, but now I am not sure (I don't even know if I trust my memory on the 'S' in the last name) . The page most likely belongs to Jim Cullen and I have been wrongly attributing the open status of these identities to Gourevitch's conjecture (special thanks to Timothy Chow for reverse-engineering my brain and revealing this very unfortunate mental hash collision).

Basically they had experimentally searched the space of identities of the form $\sum_{n=0}^{\infty} \frac{1}{P(n)}$ over a large number of polynomials $P(n)$ and used a tool like Munafo's RIES to see if they matched any known forms. They had struck gold finding some unusual identities involving either $\pi^2$ or $\pi^4$ with quadratic or quartic denominators (I don't remember which). These identities looked like they should be related to the riemann zeta function but the identities had no known proof/explanation at the time.

I want to: 

I am very happy with the answers and comments this question has generated. I think other people interested in $\pi$ formulas will probably find this as a useful exploration point.

I assume Gourevitch's Conjecture remains open although if anyone had updates on it they could post here or this more trafficked location

So a while back I was on the internet and had encountered a website containing an experimental search for identities for $\pi$. My memory was that the page belonged to either Jonathan Sondow or Michael Somos, but now I am not sure (I don't even know if I trust my memory on the 'S' in the last name) . The page most likely belongs to Jim Cullen and I have been wrongly attributing the open status of these identities to Gourevitch's conjecture (special thanks to Timothy Chow for reverse-engineering my brain and revealing this very unfortunate mental hash collision).

Basically they had experimentally searched the space of identities of the form $\sum_{n=0}^{\infty} \frac{1}{P(n)}$ over a large number of polynomials $P(n)$ and used a tool like Munafo's RIES to see if they matched any known forms. They had struck gold finding some unusual identities involving either $\pi^2$ or $\pi^4$ with quadratic or quartic denominators (I don't remember which). These identities looked like they should be related to the riemann zeta function but the identities had no known proof/explanation at the time.

1. find this website so at least I can edit this question and give the person due credit.

2. Ask what the state of those identities are. Do they remain open?

I am very happy with the answers this question has generated. I think other people interested in $\pi$ formulas will probably find this useful.

So a while back I was on the internet and had encountered a website containing an experimental search for identities for $\pi$. My memory was that the page belonged to either Jonathan Sondow or Michael Somos, but now I am not sure (I don't even know if I trust my memory on the 'S' in the last name) . The page most likely belongs to Jim Cullen and I have been wrongly attributing the open status of these identities to Gourevitch's conjecture (special thanks to Timothy Chow for reverse-engineering my brain and revealing this very unfortunate mental hash collision).

Basically they had experimentally searched the space of identities of the form $\sum_{n=0}^{\infty} \frac{1}{P(n)}$ over a large number of polynomials $P(n)$ and used a tool like Munafo's RIES to see if they matched any known forms. They had struck gold finding some unusual identities involving either $\pi^2$ or $\pi^4$ with quadratic or quartic denominators (I don't remember which). These identities looked like they should be related to the riemann zeta function but the identities had no known proof/explanation at the time.

1. find this website so at least I can edit this question and give the person due credit.

2. Ask what the state of those identities are. Do they remain open?

I am very happy with the answers and comments this question has generated. I think other people interested in $\pi$ formulas will probably find this as a useful exploration point.

I assume Gourevitch's Conjecture remains open although if anyone had updates on it they could post here or this more trafficked location