Re-phrasing the Goldbach Conjecture
It's the most famous conjecture in all of Math.
"Every even integer greater than 2 can be written as the sum of two primes."
After 282 years of research it's still unproven.
I've re-phrased it in a very visual way..
Consider any integer n greater than 2.
Notice that n is not (yet) even.
Now write all the ways of adding two integers to make n.
1+(n-1)
2+(n-2)
3+(n-3)
.....
(n-1)+1
Now regard the two columns as two lists.
Look at the list on the left.
Clearly it contains all primes less than n.
And of course so does the list on the right, which is just the same list written backward.
Goldbach says there is at least one prime in the first list, let's call it p, such that n-p is also prime.
Note: for n-p to be prime then n must be even, so the "even" part of Goldbach's conjecture is trivial.
A nice visual way to look at this is as follows:
Circle all the primes in both lists.
Now "crash" the lists together by sliding one list horizontally to "collide" with the other list.
Goldbach says the primes are distributed in such a way that there will always be at least one "prime collision".
This is a very powerful statement about the distribution of primes.
Tech Notes:
Content written and posted by Ken Abbott abbottsystems@gmail.com
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