While I was doing some research in elementary number theory I discovered some regularities that seem to be very promising.
First, function $d$ can be defined as $d(n)=d(\prod_{i=1}^{k(n)} p_i^{r_i})=\sum_{i=1}^{k(n)}r_i$ where $n= \prod_{i=1}^{k(n)} p_i^{r_i}$ is unique prime factorization of $n$ and it can be said that natural number $n>1$ is of degree $w$ if and only if $d(n)=w$.
So, for example, prime numbers are natural numbers of first degree.
The conjecture I would like to propose is the following:
Every prime number $\geq7$ is the sum of a prime number and number of second degree.
As noted in the comments, the conjecture can be rephrased very simply as:
Every prime number $p\geq 7$ can be written as $p=qr+s$ where $q,r,s$ are primes.