Checking the Harald Helfgott proof of the little Goldbach conjecture without a public release of numerical checks?

Question

A few month ago, a proof of the little/ternary Goldbach conjecture has been claimed by Harald Helfgott with three articles:

• Major arcs for Goldbach's theorem

• Minor arcs for Goldbach's theorem

• Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30

As I understand, the little Goldbach conjecture has been proven analytically in the range $[10^{30}, +\infty]$ and checked numerically in the range $[0, 10^{30}]$. I think that the proof is currently verified by referees, but I wonder how the numerical part is checked without any public release of the code. From an ethical point of view, I would think that any claim of numerical check would require the code to be publicly released. I've searched but I found nothing.

How numerical proofs are checked without access to the source code ?

Answer 1

From an ethical point of view, I would think that any claim of numerical check would require the code to be publicly released.

I think that claim is maybe a bit strong. If there is a description of the algorithm in the literature sufficiently precise for a competent expert to reconstruct the computation, then why insist on the actual source code? (Just to clarify, I totally agree that having code available would be desirable; I'm just saying that I disagree with your assertion that it is an ethical obligation.)

My cursor is hovering over the button to vote that this question be closed as "primarily opinion-based"...