Here’s a famous unsolved problem: is every even number greater than 2 the sum of 2\u00a0primes?<\/p>\n\n\n\n
The Goldbach conjecture<\/em>, dating from 1742, says that the answer is yes.<\/p>\n\n\n\n Some simple examples: What is known so far: See the reference for more details.<\/p>\n\n\n\n Presentation Suggestions:<\/strong> The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong> How to Cite this Page:<\/strong> References:<\/strong> Fun Fact suggested by: <\/strong> Here’s a famous unsolved problem: is every even number greater than 2 the sum of 2\u00a0primes? The Goldbach conjecture, dating from...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,49,116],"class_list":["post-232","page","type-page","status-publish","hentry","tag-easy","tag-prime","tag-unsolved-problem"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/232","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=232"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/232\/revisions"}],"predecessor-version":[{"id":1461,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/232\/revisions\/1461"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=232"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
4=2+2, 6=3+3, 8=3+5, 10=3+7, …, 100=53+47, …<\/p>\n\n\n\n
Schnirelmann(1930): There is some N such that every number from some point onwards can be written as the sum of at most N primes.
Vinogradov(1937): Every odd number from some point onwards can be written as the sum of 3 primes.
Chen(1966): Every sufficiently large even integer is the sum of a prime and an “almost prime” (a number with at most 2 prime factors).<\/p>\n\n\n\n
Have students suggest answers for the first few even numbers.<\/p>\n\n\n\n
This conjecture has been numerically verified for all even numbers up to several million. But that doesn’t make it true for all N… see\u00a0Large Counterexample\u00a0for an example of a conjecture whose first counterexample occurs for very large N.<\/p>\n\n\n\n
Su, Francis E., et al. “Goldbach’s Conjecture.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n
Paulo Ribenboim, The Little Book of Big Primes<\/em>, Springer-Verlag, 1991, pp.154-155.<\/p>\n\n\n\n
Lesley Ward <\/p>\n","protected":false},"excerpt":{"rendered":"