{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44403,"title":"Goldbach's marginal conjecture - Write integer as sum of three primes","description":"Goldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\r\n\r\nAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\r\n\r\nA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that \r\n\r\n\" _Every integer greater than 5 can be expressed as the sum of three primes._ \"\r\n\r\nExamples:\r\n\r\n*  6 = 2 + 2 + 2\r\n*  7 = 2 + 2 + 3\r\n*  8 = 2 + 3 + 3 \r\n*  9 = 2 + 2 + 5 = 3 + 3 + 3 \r\n* 10 = 2 + 3 + 5\r\n* 11 = 2 + 2 + 7 = 3 + 3 + 5\r\n* 12 = 2 + 3 + 7 = 2 + 5 + 5\r\n* 13 = 3 + 3 + 7 = 3 + 5 + 5\r\n* 14 = 2 + 5 + 7\r\n* 15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\r\n\r\nYour task is to write a function which takes a positive integer _n_ as input, and which returns a 1-by-3 vector _y_, which contains three numbers that are primes and whose sum equals _n_. If there exist multiple solutions for _y_, then any one of those solutions will suffice. However, _y_ must be in sorted order. You can assume that _n_ will be an integer greater than 5.\r\n\r\n","description_html":"\u003cp\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/p\u003e\u003cp\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/p\u003e\u003cp\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/p\u003e\u003cp\u003e\" \u003ci\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/i\u003e \"\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cul\u003e\u003cli\u003e6 = 2 + 2 + 2\u003c/li\u003e\u003cli\u003e7 = 2 + 2 + 3\u003c/li\u003e\u003cli\u003e8 = 2 + 3 + 3\u003c/li\u003e\u003cli\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/li\u003e\u003cli\u003e10 = 2 + 3 + 5\u003c/li\u003e\u003cli\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/li\u003e\u003cli\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/li\u003e\u003cli\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/li\u003e\u003cli\u003e14 = 2 + 5 + 7\u003c/li\u003e\u003cli\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYour task is to write a function which takes a positive integer \u003ci\u003en\u003c/i\u003e as input, and which returns a 1-by-3 vector \u003ci\u003ey\u003c/i\u003e, which contains three numbers that are primes and whose sum equals \u003ci\u003en\u003c/i\u003e. If there exist multiple solutions for \u003ci\u003ey\u003c/i\u003e, then any one of those solutions will suffice. However, \u003ci\u003ey\u003c/i\u003e must be in sorted order. You can assume that \u003ci\u003en\u003c/i\u003e will be an integer greater than 5.\u003c/p\u003e","function_template":"function y = goldbach3(n)\r\n  y = [n,n,n];\r\nend","test_suite":"%%\r\nn = 6;\r\ny = goldbach3(n);\r\ny_correct = [2,2,2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 7;\r\ny = goldbach3(n);\r\ny_correct = [2,2,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = goldbach3(n);\r\ny_correct = [2,3,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 9;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,5];\r\ny_correct2 = [3,3,3];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 10;\r\ny = goldbach3(n);\r\ny_correct = [2,3,5];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,7];\r\ny_correct2 = [3,3,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 12;\r\ny = goldbach3(n);\r\ny_correct1 = [2,3,7];\r\ny_correct2 = [2,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 13;\r\ny = goldbach3(n);\r\ny_correct1 = [3,3,7];\r\ny_correct2 = [3,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 14;\r\ny = goldbach3(n);\r\ny_correct = [2,5,7];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 15;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,11];\r\ny_correct2 = [3,5,7];\r\ny_correct3 = [5,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2)|isequal(y,y_correct3))\r\n\r\n%%\r\nn = 101;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%%\r\nn = 102;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nfor n = 250:300\r\n    y = goldbach3(n);\r\n    assert(isequal(y,sort(y)));\r\n    assert(all(isprime(y)));\r\n    assert(sum(y)==n);\r\nend\r\n\r\n%%\r\nn = randi(2000)+5; % generate a random integer greater than 5 and smaller than 2006\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nvalid = zeros(1,50);\r\nfor k = 1:50\r\n    n = randi(1000)+5; % generate a random integer greater than 5 and smaller than 1006\r\n    yk = goldbach3(n);\r\n    valid(k) = (isequal(yk,sort(yk)) \u0026 all(isprime(yk)) \u0026 sum(yk)==n);\r\nend\r\nassert(all(valid));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":108199,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":75,"test_suite_updated_at":"2017-11-18T23:12:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-11-14T00:05:38.000Z","updated_at":"2026-03-16T15:38:02.000Z","published_at":"2017-11-14T01:21:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2 + 2 + 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e7 = 2 + 2 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e10 = 2 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e14 = 2 + 5 + 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task is to write a function which takes a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as input, and which returns a 1-by-3 vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains three numbers that are primes and whose sum equals\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If there exist multiple solutions for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then any one of those solutions will suffice. However,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e must be in sorted order. You can assume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be an integer greater than 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44403,"title":"Goldbach's marginal conjecture - Write integer as sum of three primes","description":"Goldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\r\n\r\nAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\r\n\r\nA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that \r\n\r\n\" _Every integer greater than 5 can be expressed as the sum of three primes._ \"\r\n\r\nExamples:\r\n\r\n*  6 = 2 + 2 + 2\r\n*  7 = 2 + 2 + 3\r\n*  8 = 2 + 3 + 3 \r\n*  9 = 2 + 2 + 5 = 3 + 3 + 3 \r\n* 10 = 2 + 3 + 5\r\n* 11 = 2 + 2 + 7 = 3 + 3 + 5\r\n* 12 = 2 + 3 + 7 = 2 + 5 + 5\r\n* 13 = 3 + 3 + 7 = 3 + 5 + 5\r\n* 14 = 2 + 5 + 7\r\n* 15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\r\n\r\nYour task is to write a function which takes a positive integer _n_ as input, and which returns a 1-by-3 vector _y_, which contains three numbers that are primes and whose sum equals _n_. If there exist multiple solutions for _y_, then any one of those solutions will suffice. However, _y_ must be in sorted order. You can assume that _n_ will be an integer greater than 5.\r\n\r\n","description_html":"\u003cp\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/p\u003e\u003cp\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/p\u003e\u003cp\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/p\u003e\u003cp\u003e\" \u003ci\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/i\u003e \"\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cul\u003e\u003cli\u003e6 = 2 + 2 + 2\u003c/li\u003e\u003cli\u003e7 = 2 + 2 + 3\u003c/li\u003e\u003cli\u003e8 = 2 + 3 + 3\u003c/li\u003e\u003cli\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/li\u003e\u003cli\u003e10 = 2 + 3 + 5\u003c/li\u003e\u003cli\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/li\u003e\u003cli\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/li\u003e\u003cli\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/li\u003e\u003cli\u003e14 = 2 + 5 + 7\u003c/li\u003e\u003cli\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYour task is to write a function which takes a positive integer \u003ci\u003en\u003c/i\u003e as input, and which returns a 1-by-3 vector \u003ci\u003ey\u003c/i\u003e, which contains three numbers that are primes and whose sum equals \u003ci\u003en\u003c/i\u003e. If there exist multiple solutions for \u003ci\u003ey\u003c/i\u003e, then any one of those solutions will suffice. However, \u003ci\u003ey\u003c/i\u003e must be in sorted order. You can assume that \u003ci\u003en\u003c/i\u003e will be an integer greater than 5.\u003c/p\u003e","function_template":"function y = goldbach3(n)\r\n  y = [n,n,n];\r\nend","test_suite":"%%\r\nn = 6;\r\ny = goldbach3(n);\r\ny_correct = [2,2,2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 7;\r\ny = goldbach3(n);\r\ny_correct = [2,2,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = goldbach3(n);\r\ny_correct = [2,3,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 9;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,5];\r\ny_correct2 = [3,3,3];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 10;\r\ny = goldbach3(n);\r\ny_correct = [2,3,5];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,7];\r\ny_correct2 = [3,3,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 12;\r\ny = goldbach3(n);\r\ny_correct1 = [2,3,7];\r\ny_correct2 = [2,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 13;\r\ny = goldbach3(n);\r\ny_correct1 = [3,3,7];\r\ny_correct2 = [3,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 14;\r\ny = goldbach3(n);\r\ny_correct = [2,5,7];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 15;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,11];\r\ny_correct2 = [3,5,7];\r\ny_correct3 = [5,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2)|isequal(y,y_correct3))\r\n\r\n%%\r\nn = 101;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%%\r\nn = 102;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nfor n = 250:300\r\n    y = goldbach3(n);\r\n    assert(isequal(y,sort(y)));\r\n    assert(all(isprime(y)));\r\n    assert(sum(y)==n);\r\nend\r\n\r\n%%\r\nn = randi(2000)+5; % generate a random integer greater than 5 and smaller than 2006\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nvalid = zeros(1,50);\r\nfor k = 1:50\r\n    n = randi(1000)+5; % generate a random integer greater than 5 and smaller than 1006\r\n    yk = goldbach3(n);\r\n    valid(k) = (isequal(yk,sort(yk)) \u0026 all(isprime(yk)) \u0026 sum(yk)==n);\r\nend\r\nassert(all(valid));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":108199,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":75,"test_suite_updated_at":"2017-11-18T23:12:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-11-14T00:05:38.000Z","updated_at":"2026-03-16T15:38:02.000Z","published_at":"2017-11-14T01:21:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2 + 2 + 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e7 = 2 + 2 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e10 = 2 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e14 = 2 + 5 + 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task is to write a function which takes a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as input, and which returns a 1-by-3 vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains three numbers that are primes and whose sum equals\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If there exist multiple solutions for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then any one of those solutions will suffice. However,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e must be in sorted order. 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