I think a better form of this conjecture is:

" Every prime number p=>19
can be written as p=2*p1 + 3*p2

where p1 & p2 are odd primes. "

Note that 19 is the smallest number of the form
2*p1 + 3*p2 where p1 & p2 are

distinct odd primes.

It seems that like the Goldbakh's conjecture,
the proof is difficult or impossible

at this age.

...as Gauss said: "*I can frame
infinitely many propositions of that type, that never will be
contradicted*" (*)

This one is much simpler: "Every p=p2-p1 +1"

Or this: "p = p1 + p2 + p3 ; p>7", proved by Vinogradov.

Or this :"Every p = p(n+1)- p(n) + 1"

Or this :"For every p there is an n >=0 that makes 6(p - n^2) + 1 a
prime.

________

(*) *I confess that Fermat's Theorem as an
isolated proposition has very little interest for me, because I could
easily lay down a multitude of such propositions, which one could
neither prove nor dispose of*.[A reply to Olbers' attempt in 1816 to
entice him to work on Fermat's Theorem.].Quoted in J R Newman, *The
World of Mathematics* (New York 1956).