3
$\begingroup$

In his proof of the ternary Goldbach conjecture, H.A. Helfgott says that it has been verified that every odd number less than $N_0 = 10^{30}$ is the sum of at most 3 primes. How would one verify this up to $N_0$ in a reasonable amount of time. This is because even if one could verify in $O(1)$ time whether or not a number is the sum of 3 primes, to verify it until $10^{30}$ would still take a very long time.

$\endgroup$
2
$\begingroup$

See http://arxiv.org/pdf/1305.3062.pdf for a detailed description of how the verification was obtained. It's pretty heavy though, as can be expected because naive verification would take far too long.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.