Can every even integer be expressed as the difference of two primes?

Can every even integer be expressed as the difference of two primes? If so, is there any elementary proof?

This is listed as an open question at the Prime Pages: http://primes.utm.edu/notes/conjectures/

This follows from Schinzel's conjecture H. Consider the polynomials $x$ and $x+2k$. Their product equals $2k+1$ at 1 and $4(k+1)$ at 2, which clearly do not have any common divisors. So if Schinzel's conjecture holds, there are infinitely many numbers $n$ such that the polynomials are both prime at $n$, and so subtracting gives the result.

Why are removable discontinuities even discontinuities at all?

$L^p$-norm of a non-negative measurable function

What is $\lim_{n\to \infty}\sum_{k=1}^n \left(\frac{k}{n}\right)^n$? [duplicate]

What's the generalisation of the quotient rule for higher derivatives?

Methods to evaluate $ \int _{a }^{b }\!{\frac {\ln \left( tx + u \right) }{m{x}^{2}+nx +p}}{dx} $

series involving $\log \left(\tanh\frac{\pi k}{2} \right)$

Question about Angle-Preserving Operators

Relation of this antisymmetric matrix $r = \left(\begin{smallmatrix}0 &1\\-1&0\end{smallmatrix}\right)$ to $i$

The ring $ℤ/nℤ$ is a field if and only if $n$ is prime

Prove $\mathbb{Z}$ is not a vector space over a field

A natural proof of the Cauchy-Schwarz inequality

Question about connection between Poisson and Gamma distributions