Are prime numbers among sums of prime numbers distributed as $\frac n{2\ln(n)}$ ?

Exact formalization occurrence from the upstream source collection.

Source category: research open
Formal proof: Not retained
Vela current state: No Repository Result attached

Tracked question

The conjecture claims that

\pi_n\sim\frac n{2\ln(n)}

. In other words, primes are distributed among the much sparser sequence

(S_n)_n

with essentially the same density as in the positive integers, up to a factor of

2

. MathOverflow 434111. [Me18] Meštrović, R., *Curious Conjectures on the Distribution of Primes Among the Sums of the First 2n Primes*, arXiv:1804.04198 (2018).

Lean declaration

Open source view

theorem restricted_prime_number_theorem :
    answer(sorry) ↔ ((fun n : ℕ => (piRestricted n : ℝ)) ~[atTop] (fun n : ℕ => (n : ℝ) / (2 * Real.log n)))

Question

Lean declaration

Search problems.science