The sequence
$$a(n)=\sum_{k=2}^n \varphi(k)$$
has, in the range $2 \leq n\leq 10$ a total of $5$ primes.
It has $36$ primes in the range $2 \leq n\leq 100$.
$203$ primes in the range $2 \leq n\leq 1000$ and, $1348$ primes in the range $2 \leq n\leq 10000$.
As expected, primes are becoming less dense, but, there is still much of them.
Are there any properties of totient function that guarantee us an infinite number of primes in this sequence?
It is known that $\varphi(n)$ is even for $n \geq 3$.
This is really hard (as noted in the comment) and the methods may be still unavailable, I even do not know how to heuristically justify this.