Are prime numbers among sums of prime numbers distributed as `n/2ln(n)`?

### What is the conjecture
Primes seem to be far more likely to appear among sums of primes compared to the average distribution given by the prime number theorem. The conjecture describes an explicit distribution which is backed by numerical computations. It appeard independently on [MathOverflow](https://mathoverflow.net/questions/434111/are-prime-numbers-among-sums-of-prime-numbers-distributed-as-frac-n2-lnn) and on [arXiv](https://arxiv.org/abs/1804.04198).

Status: open

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-11

### Choose either option
- [X] I plan on adding this conjecture to the repository
- [ ] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading the conjecture statement in this issue and the repository's existing formalized conjectures in the AMS-11 area. Determine the appropriate Lean representation and verify the resulting statement against the cited MathOverflow and arXiv references; done means the conjecture is added to the repository and accepted by its checks.

Written by the indexing model from the issue text.