An Arithmetic Solution to the Goldbach Conjecture(adsbygoogle = window.adsbygoogle || []).push({});

Prove that any and every even integer >4 may be expressed as the sum of at least some 2 prime integers.

Proof D.

1. We may regard prime integer multiplication as being equivalent to prime integer summation, i.e. 2x3=2+2+2

2. Therefore, given the Fundamental Theorem of Arithmetic, any and every even integer >4 may be expressed as the summation of a series of prime integers, i.e.,

I = Pa+…+Pb+…+Pc+…

where I is any integer >1 and P is some prime integer

3. Any and every even integer must equal the summation of some two odd integers, therefore

E = Oa +Ob

where E is any and every even number and O is some odd integer.

4. Given the FTOA it must also be the case that for any even integer >4

E = Pa+…+Pb+…+Pc+…

5. Therefore for any and every even integer >4

Pa+…+Pb+…+Pc+…= E = Oa +Ob [4]

6. Therefore the sum Oa + Ob must equal a summation of a series of primes.

7. Since there are at least two addends comprising the Oa +Ob summation then each addend is allowed to be a prime number.

8. E, in this case, must meet two conditions:

a. E must be composed of 2 and only 2 odd integers.

b. E must be a summation of primes.

9. In order to satisfy both conditions a and b then it must be the case that the two odd integers, Oa and Ob must sum as primes where

Pa+Pb = E= Oa +Ob [5]

10. Therefore any and every even integer >4 may be expressed as the sum of at least some 2 prime integers.

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