Goldbach's weak conjecture

Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.) This is called Goldbach's weak conjecture. I think that it is almost the same as Goldbach's conjecture.

a＞2
2a+1=P1+P2+P3
2a=(P1+P2+P3)-1

P is prime numbers.

a＞2
2a+1=O1+O2+O3
2a=(O1+O2+O3)-1

O is odd numbers.



For example,

2a=6 (a=3)

6=(3+2+2)-1 This is prime numbers.

6=(3+3+1)-1=(5+1+1)-1 This is odd numbers.


2a=8 (a=4)

8=(5+2+2)-1=(3+3+3)-1 This is prime numbers.

8=(7+1+1)-1=(5+3+1)-1=(3+3+3)-1 This is odd numbers.


2a=10 (a=5)

10=(7+2+2)-1=(5+3+3)-1 This is prime numbers.

10=(5+5+1)-1=(7+3+1)-1=(9+1+1)-1=(5+3+3)-1 This is odd numbers.

∴ (P1+P2+P3)-1⊂(O1+O2+O3)-1⊂2a


Therefore, Goldbach's weak conjecture is correct.




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