Question

Primes: Something maybe interesting. Can somebody approve or debunk this?

Answer 1

This is a special case of the Goldbach Conjecture, a famous unsolved problem. If an even number 2n is halfway between the two primes 2n-a and 2n+a, then that's equivalent to the number 4n being the sum of those two primes.

So your observation is the same as the Goldbach Conjecture for multiples of four, rather than for all even numbers.

Answer 2

Interesting!
Never thought of that.

If your conjecture is true for all numbers then you have world fame forever.

For even numbers the distance would always be odd. For odd numbers the distance would always be even.

On the bright side, if GC is false the number that disproves it would be extremely large. And your conjecture would also fail on that number.

I feel it’s likely GC is correct and so is your pattern.

Answer 3

Good luck proving this, haha.

Answer 4

>Every even natural number greater than 2 has at least one 1 pair of primes (both numbers) that are equally distanced from this even natural number.

This is probably true for every number greater than two, as that would be corollary of the Goldbach conjecture. But we cannot prove that right now, some technology for that is missing.

Answer 5

Lol I found that on my own too when I was bored in class. It is equivalent to Goldbach's Conjecture bc if for all natural integer n, there exist p and q primes such that 2n = p + q.
Then n + n = p + q
And n - p = - (n - q).

Answer 6

The distance number is not always a prime. 20-9=11 and 20+9=29 are both prime.