{"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":2910,"title":"Mersenne Primes vs. All Primes","description":"A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003chttps://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes Problem 525\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\r\n\r\nFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.","description_html":"\u003cp\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"\u003eProblem 525\u003c/a\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/p\u003e\u003cp\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/p\u003e","function_template":"function [y,f] = Mersenne_prime_comp(n)\r\n y = 1;\r\n f = 0;\r\nend","test_suite":"%%\r\nn = 1e2;\r\ny_correct = 3;\r\nf_correct = 3/25;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(isequal(f,f_correct))\r\n\r\n%%\r\nn = 1e3;\r\ny_correct = 4;\r\nf_correct = 0.023809523809524;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e4;\r\ny_correct = 5;\r\nf_correct = 0.004068348250610;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e5;\r\ny_correct = 5;\r\nf_correct = 5.212677231025855e-04;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e6;\r\ny_correct = 7;\r\nf_correct = 8.917424647761727e-05;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":846,"test_suite_updated_at":"2015-02-01T04:14:08.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:56:07.000Z","updated_at":"2026-04-01T10:02:01.000Z","published_at":"2015-02-01T04:14:08.000Z","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\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\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\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\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":2910,"title":"Mersenne Primes vs. All Primes","description":"A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003chttps://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes Problem 525\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\r\n\r\nFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.","description_html":"\u003cp\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"\u003eProblem 525\u003c/a\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/p\u003e\u003cp\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/p\u003e","function_template":"function [y,f] = Mersenne_prime_comp(n)\r\n y = 1;\r\n f = 0;\r\nend","test_suite":"%%\r\nn = 1e2;\r\ny_correct = 3;\r\nf_correct = 3/25;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(isequal(f,f_correct))\r\n\r\n%%\r\nn = 1e3;\r\ny_correct = 4;\r\nf_correct = 0.023809523809524;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e4;\r\ny_correct = 5;\r\nf_correct = 0.004068348250610;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e5;\r\ny_correct = 5;\r\nf_correct = 5.212677231025855e-04;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e6;\r\ny_correct = 7;\r\nf_correct = 8.917424647761727e-05;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":846,"test_suite_updated_at":"2015-02-01T04:14:08.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:56:07.000Z","updated_at":"2026-04-01T10:02:01.000Z","published_at":"2015-02-01T04:14:08.000Z","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\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\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\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. 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