1. For the first even number 12 = 3+3+3+3.
We allow justice for the previous N> 5: p1 + p2 + p3 + p4 =2N  We will add to both parts on 1 p1 + p2 + p3 + p4 +1 =2N +1  where on the right the odd number also agrees  p1 + p2 + p3 + p4 +1= p5 + p6 + p7 
Having added to both parts still on 1
p1 + p2 + p3 + p4 + 2= p5 + p6 + p7 +1  We will unite p6 + p7 +1 again we have some odd number,
which according to  we replace with the sum of three simple and as a result we receive: p1 + p2 + p3 + p4 + 2= p5 + p6 + p7 + p8  at the left the following even number is relative , and on the right the sum
four prime numbers. p1 + p2 + p3 + p4 = 2N 
Thus obvious performance of an inductive mathematical method. As was to be shown.
This is item 1. Previous 12 next14, previous 14 next 16 i mat. induction.