Is there an algorithm help us to write each even number as sum of primes numbers? 1) Is there an algorithm help us to  write each even number as sum of primes numbers :
for example :$4=2+2$
$8=3+5$
where : $3,5,2$ are primes 
2) why we couldn't writing all odd numbers as sum of primes?
Late Edit: example look :$7=3+2+2$ 
I would be interest for any replies or any comments

It is Goldbach's conjecture that every even number greater than 2 is the sum of two primes.  
Last year Harald Helfgott proved that every odd number greater than 5 is the sum of three primes.  
For the last decade, Tomás Oliveira e Silva has run distributed calculations to verify the Goldbach conjecture into the quintillions.
I have no idea about the algorithms.
