I made some numerical simulations about the number of primes which are the sum of 3 consecutive primes ([OEIS A034962][1]), that is for instance:
$$5+7+11=23$$
$$7+11+13=31$$
$$11+13+17=41$$
$$17+19+23=59$$
$$19+23+29=71$$
$$23+29+31=83$$
$$29+31+37=97$$
$$...$$
The number of such triplets, till a certain integer n, seems to be well approximated by the following function:
$$\frac{e\cdot\pi(n)}{\log(n)}$$

> If the previous was true, the density of such primes in the whole set
> of prime numbers would be comparable to that of primes inside the set
> of naturals.
> 
> **I ask if this estimate is correct and some references about this matter.**

Thanks.


  [1]: https://oeis.org/A034962