Goldbach's Weak Conjecture

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Theorem

Every odd integer greater than $7$ is the sum of three odd primes.

Proof


Also known as

It is also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem


Historical Note

  • 2002: Liu Ming-Chit and Wang Tian-Ze lowered the threshold for Vinogradov's result to approximately $n > e^{3100}$, which is roughly $2 \times 10^{1346}$. This gives an upper bound such that it is feasible to test any single odd number below that threshold. Though one can calculate: if a modern desktop were the size of a 1cm cube, one filled the solar system with such cubes and left them running the fastest known algorithms since the beginning of time, numbers larger than $10^{70}$ would remain untested. For this reason the problem is still considered unsolved, though the existence of only finitely many counterexamples is a worthwhile result in its own right.


Also see


Source of Name

This entry was named for Christian Goldbach.