Inferences from Gold Bach’s Conjuncture

Gold Bach’s Conjuncture is as given below ( Not given rigorously) ..
e ==> even number
p ==> prime number

o ==> odd number
According to Gold Bach,
Any even number can be written as a sum of two different primes.

Now lets get into my observations...
Using Gold Bach’s conjecture
Any e = p1+p2, where p1 and p2 are two different prime numbers
Now take any prime number p

2p is an even number,
So 2p = p1 + p2 using Goldbachs conjuncture where p1 and p2 are two different primes
So,
p = (p1+p2)/2

Inference1:
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There fore any prime number can be written as the average of two different primes.
Eg:
Take 17
2*17 = 34 = 31+3
There fore 17 = (31+3)/2
This also means that any prime number is equidistant from two some other two primes
This inference shows the uniformity of the primes though they cant be represented by a single
formulae

Inference2:
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Since p = (p1+p2)/2, using the above inference,
p1 can be a maximum of 2p-1 so that the other prime can be a minimum of 1
The p1 be a minimum of p+2 and p2 can be a minimum of p-2 so that their average is p

From this we can see that if p is any prime, there is at least
one prime number between p and 2p

Eg:
Take p = 3
Here 2p =6
So there is a prime 5 between 3 and 6
Another Eg:
Take 31 and 2*31 = 62
Between 31, there are primes 37, 43 etc...