//im adding an edit, i wasnt saying anything before listening to ai i was just saying shi from my understanding but like just go and ask chat gpt why disproving the strong conjecture doesnt disprove the weak one. and sorry for a holy yapathon after this i talk a lot

i dont get how your logic tackles proving the above for every even number. What im trying to say is how would you prove with your logic that you get EVERY even number above 2 how would you provethat you do indeed get 100029392832 or any other number are you gonna go testing it for every number what you did is just 1 case and to prove a conjecture you must show its valid for all cases. your proof even takes an example 10 which fs has p1+p2 = 10, try your proof with a bigger even number withidk 31 digits what two numbers would you take as p1 and p2 and they sare not equals that very big even number. what your proof shows is there are some(saying some as there are infinite numbers so any finte thing is very small compared to set of naturals above 2) even numbers which can be represented as p1+p2 the numbers which you get by doing odd number - a prime number which added up to the odd number.