====== Goldbach's conjecture ====== Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states: // Every even integer greater than 2 can be expressed as the sum of two primes.// The conjecture has been shown (by computerised testing) to hold for all integers less than 4 × 1018, but remains unproven for all possible numbers. __ BROKEN-LINK:[[http://primes.utm.edu/glossary/page.php?sort=GoldbachConjecture|Further reading]] LINK-BROKEN __ courtesy Mathematics and Statistics dept. University Tennessee at Martin, US Goldbach's [[http://eulerarchive.maa.org//correspondence/letters/OO0765.pdf|original letter]] to Euler in 1742. ---- Note that Goldbach's //weak// conjecture (a.k.a Goldbach's odd conjecture) //Every odd number greater than 7 can be expressed as the sum of three odd primes// is generally accepted to have been finally proved in 2013, by [[http://www.humboldt-professur.de/en/preistraeger/preistraeger-2015/helfgott-harald-andres|Harald Helfgott]]