{"id":136,"date":"2008-10-22T01:45:29","date_gmt":"2008-10-22T06:45:29","guid":{"rendered":"http:\/\/mariusbancila.ro\/blog\/?p=136"},"modified":"2008-10-22T01:46:09","modified_gmt":"2008-10-22T06:46:09","slug":"even-numbers-as-sum-of-2-primes","status":"publish","type":"post","link":"https:\/\/mariusbancila.ro\/blog\/2008\/10\/22\/even-numbers-as-sum-of-2-primes\/","title":{"rendered":"Even numbers as sum of 2 primes"},"content":{"rendered":"

A very old unsolved problem in numbers theory, known as Goldbach’s conjecture<\/a>, says that any even number greater than 5 can be written as the sum of 2 prime numbers. It hasn’t been solver yet, not I will try to solve it. But I decided to write some F# code to display all the possibilities of writing an even number as the sum of two primes. This turned to be quite simple actually:<\/p>\n

First, I wrote a function that checks if a number is prime:<\/p>\n

let is_prime n =\r\n   not ([2..n\/2] |> Seq.filter (fun x -> (n % x) = 0) |> Seq.nonempty)\r\n<\/pre>\n
Then it was all about checking all the numbers from 2 to N\/2 to see if k and N-k are both primes and if so print them:<\/p>\n
let check n =\r\n   [2..n\/2] |>\r\n   Seq.filter (fun x -> (is_prime x) && (is_prime (n-x))) |>\r\n   Seq.iter (fun x -> printfn \"%d & %d\" x (n-x))\r\n<\/pre>\n
For instance, if we consider number 200, the check function would print:<\/p>\n
3 & 197
\n7 & 193
\n19 & 181
\n37 & 163
\n43 & 157
\n61 & 139
\n73 & 127
\n97 & 103<\/p><\/blockquote>\n
And that’s about it; though you can imagine optimizing this by caching the prime numbers already computed. But that wasn’t something I wanted to consider for this problem.<\/p>\n","protected":false},"excerpt":{"rendered":"
A very old unsolved problem in numbers theory, known as Goldbach’s conjecture, says that any even number greater than 5 can be written as the sum of 2 prime numbers. It hasn’t been solver yet, not I will try to solve it. But I decided to write some F# code to display all the possibilities … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[37],"tags":[],"class_list":["post-136","post","type-post","status-publish","format-standard","hentry","category-fsharp"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t