Goldbach Conjecture 2017 or Conjecture of Preservation of Nature of Numbers

According to Wikipedia:

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. 

https://en.wikipedia.org/wiki/Goldbach's_conjecture

On Wikipedia and also in other articles I found the following claim about the Goldbach Conjecture:

"The best known result is due to Olivier Ramaré, who in 1995 showed that every even number n  ≥ 4 is in fact the sum of at most six primes.".

About this legation I think:

Or, this is wrong. Or, this is badly formulated.


The number 124, for example, is the sum of 8 prime numbers.

5+7+11+13+17+19+23+29 = 124

That is, it has already exceeded that maximum sum of 6 prime numbers.


In the example below I made the sum of all primes less than 100

Sum of arithmetic progression of prime numbers less than 100:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

5+7
Number 12 (It's a number even. It is the sum of 2 prime numbers)

5+7+11+13
Number 36 (It's a number even. It is the sum of 4 prime numbers)

5+7+11+13+17+19
Number 72 (It's a number even. It is the sum of 6 prime numbers)

5+7+11+13+17+19+23+29
Number 124 (It's a number even. It is the sum of 8 prime numbers)

5+7+11+13+17+19+23+29+31+37
Number 192 (It's a number even. It is the sum of 10 prime numbers)

5+7+11+13+17+19+23+29+31+37+41+43
Number 276 (It's a number even. It is the sum of 12 prime numbers)

5+7+11+13+17+19+23+29+31+37+41+43+47+53
Number 376 (It's a number even. It is the sum of 14 prime numbers)

5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61
Number 496 (It's a number even. It is the sum of 16 prime numbers)

5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71
Number 634 (It's a number even. It is the sum of 18 prime numbers)

5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79
Number 786 (It's a number even. It is the sum of 20 prime numbers)

5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83+89
Number 958 (It's a number even. It is the sum of 22 prime numbers)

As we can see there is no limit. Besides that:

"The sum of the arithmetic progression of the prime numbers results in an alternation between even and odd numbers.".

Example:

2+3              = 5 odd
2+3+5            = 10 even
2+3+5+7          = 17 odd
2+3+5+7+11       = 28 even
2+3+5+7+11+13    = 41 odd
2+3+5+7+11+13+17 = 58 even

That is, the sum of the progression results in an odd number, then even, then odd, etc.

The same thing happens with odd numbers:

1+3= 4 even
1+3+5= 9 odd
1+3+5+7= 16 even
1+3+5+7+9= 25 odd

We can also see that:

The sum of 2 prime numbers results in an even number.
The sum of 3 prime numbers results in an odd number.
The sum of 4 prime numbers results in an even number.
The sum of 5 prime numbers results in an odd number.
Since, n greater than 2.

Considering this we can create these Conjectures:

"The sum of an amount even of prime numbers results in an even number.".

"The sum of an amount odd of prime numbers results in an odd number".

Since, n greater than 2.

In other words: water with water can not generate fire.

Or, as we learned in preschool:
Even with Even -> Equal nature - > Generates Even.
Odd with Odd  -> Equal nature  -> Generates Even.
Even with Odd  -> Different nature  -> Generates Odd.
Odd with Even  ->Different nature  -> Generates Odd

So:

Goldbach conjecture

"Every even integer greater than 2 can be expressed as the sum of two primes".

It is equivalent to:

Goldbach Conjecture 2017 or Conjecture of Preservation of Nature of Numbers

"Every EVEN integer greater than 2 can be expressed as the sum of an amount EVEN of prime numbers".