Just like the Collatz 3n + 1 Conjecture and the Riemann Hypothesis, there are heuristic probabilistic arguments which support Goldbach's Conjecture
, and Goldbach's Conjecture
has been verified by computers for a large number of even numbers .
. Every even number can be written as the sum of two primes.
For example, in Uncle Petros & Goldbach's Conjecture
. Mathematical Obsession (Doxiadis, 2000), consider the portrayal of Uncle Petros (a mathematician): the black sheep of the family (p.3), one of "life's failures" (p.3), has "no social life of any kind" (p.6), and, yet, a "phenomenal, unprecedented mathematical talent" (p.19).
He and Godel both turn up as characters in Apostolos Doxiadis's 1992 novel Uncle Petros and Goldbach's Conjecture
, of which an English translation was published last year to considerable success.
On my eleventh birthday, I read an article in the Chicago Tribune that reported on a contest with a $1 million prize for anyone who could prove Goldbach's conjecture
. The article went on to state the conjecture as "Every even number is the sum of two prime numbers." In under five minutes, I discovered a disproof of Goldbach's conjecture
as stated in the article.
"Your uncle, my son," he says to the narrator, "committed the greatest of sins." The "sin" is that Uncle Petros squandered his God-given talent by wasting his time trying to prove Goldbach's Conjecture
. The father calls it "a riddle of some sort, something of no interest to anyone except a handful of idlers playing intellectual games." The Conjecture, of course, unsolved for more than two centuries, is predicated on the relatively simple claim that every number greater than two is the sum of two primes.