Question

how is this ?

Answer 1

1. substitution
- let p and k , two prime numbers greater or equal 2,from the set of prime numbers, P,
in the form : p=2a + 1 and k=2b + 1 , such that a and b are natural numbers,from the set of natural numbers N,
- let m=2n ,m greater or equal 4,even number,from the set of natural numbers N and n grater or equal 2,natural number from set of natural numbers N,
2. conclusion
- every even integer greater than 2 can be expressed as the sum of two primes
3. demonstration
* - step 0. for n=2 --- m=4 --- 4=2+2
** - step 1. for - if n is greater or equal 3 so always will be a number a and b such that
n=a + b + 1
- dem. 3=1+1+1 4=2+1+1
5=2 +2+1 ................ n=a+b+ 1
- so for n=k than k=a+b+1 - suppose that is true
- for k+1=(a+b+1)+1=(k)+1=k+1
- so for k+1 is true
- for n grater than 2 always will be a number a and b such that n =a+b+ 1
*** - step 2.
- every even integer greater than 4 can be expressed as the sum of two primes
m=p+k
- demonstration by ,,reductio ad absurdum"
- so than m is not equal p+k
- so than 2n is not equal 2a+1+2b+1
- so than 2n is not equal 2a+2b+2 / divide both sides by 2
- so than n is not equal a+b+1 - so but n=a+b+1 was proved that is true
- so than m=p+k is proved that is true

Answer 2

Are we trying to prove:

every even integer greater than 2 can be expressed as the sum of two primes??

Answer 3

- yes here is proven that is true sure