Every mathematician is taught that prime numbers are the multiplicative building blocks of all integers. In other words: every integer can be expressed as a multiplication of one or more prime numbers less than or equal to its value.
However, what of addition? Can every integer also be expressed as the sum of two prime numbers? In mathematical terms that question, known as the Marginal Conjecture, would be expressed by the following hypothesis:
∀(z ∈ ℕ){∃(x,y ∈ P){(x ≠ y) ∧ (x + y = z)}}
And such a mathematical statement would be interpreted as follows:
∀(z ∈ ℕ) FOR EVERY NATURAL INTEGER
∃(x,y ∈ P) THERE EXIST TWO PRIMES NUMBERS
(x ≠ y) SUCH THAT THE PRIMES ARE DISTINCT
(x + y = z) AND SUCH THAT THEIR SUM IS THAT INTEGER
I have no idea if it is possible to prove or disprove the above hypothesis, nor do I really have the free time to find out. It has held up for the first few integers I have tried it on, but that is nowhere near a guarantee of its veracity.
If given a little time, I could easily devise a somewhat inefficient algorithm capable of testing it, but that must unfortunately wait until later. In the interim, anyone who would like to put it to the test on their own is free to do so.
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