/sci/ - Science & Math

[Anonymous No.6493374]

I have a question about the Goldbach conjecture.

Basically, it asks whether all even integers greater than 2 can be represented as the sum of two primes.

so, for some p,q, if p and q are prime, then for all n >= 2, p+q = 2n

so say n = 2, then p+q = 4, so p,q = 2, since 2 is prime

now lets say n > 2. since all other primes are odd by definition and the sum of two odd integers is an even integer, we can see that the sum of two primes is an even integer. Same works for subtraction.

Is it reasonable to claim that for some n and for some primes p,q, 2n - q = p? Has this been verified? Essentially I'm asking that if we take any even integer and subtract a prime less than the even integer, is the result a prime?

[Anonymous No.6493386]

>Essentially I'm asking that if we take any even integer and subtract a prime less than the even integer, is the result a prime?
obviously not anon.

[Anonymous No.6493392]

the question you are probably after is: given any even integer n >= 4 does there exist a prime p such that q = n - p is prime?