// Numbas version: finer_feedback_settings
{"name": "Proof 1: the Goldbach conjecture (multiple choice)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Proof 1: the Goldbach conjecture (multiple choice)", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "parts": [{"showCorrectAnswer": true, "prompt": "<p>Prove that it is possible to write $\\var{2a}$ as a sum of two primes, by actually writing it as sum of two primes:</p>", "showCellAnswerState": true, "matrix": ["1", 0, 0], "minMarks": 0, "displayColumns": 0, "shuffleChoices": false, "extendBaseMarkingAlgorithm": true, "marks": 0, "distractors": ["Correct Answer", "$1$ is not prime", "2 is not prime"], "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "unitTests": [], "maxMarks": 0, "showFeedbackIcon": true, "displayType": "radiogroup", "choices": ["$\\var{answers[keys(answers)[a]]}$", "{2a-1}+1", "{2a-2} + 2"], "customMarkingAlgorithm": "", "type": "1_n_2"}], "variable_groups": [], "ungrouped_variables": ["a", "answers", "A0", "A1", "A2", "A3"], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..12)"}, "answers": {"name": "answers", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "[\"0\":\"0+0\",\"2\":\"1+1\",\"4\":\"2+2\",\"6\":\"3+3\",\"8\":\"3+5\",\"10\":\"5+5\",\"12\":\"5+7\",\"14\":\"7+7\",\"16\":\"11+5\",\"18\":\"11+7\",\"20\":\"13+7\",\"22\":\"5+17\",\"24\":\"5+19\",\"26\":\"19+7\",\"28\":\"17+11\",\"30\":\"17+13\"]"}, "A2": {"name": "A2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "answers[\"\" + 2(a+2)]"}, "A3": {"name": "A3", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "answers[\"\" + 2(a+3)]"}, "A0": {"name": "A0", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "answers[\"\" + 2(a+0)]"}, "A1": {"name": "A1", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "answers[\"\" + 2(a+1)]"}}, "metadata": {"description": "<p>Intorduction to proof and existence statements.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "preamble": {"css": "", "js": ""}, "statement": "<p>In 1742, Christian Goldbach wrote in a letter to Leonhard Euler that</p>\n<p style=\"text-align: center;\">Every even integer greater than 2 can be written as the sum of two primes.</p>\n<p style=\"text-align: left;\">This is now called Goldbach's conjecture, and is the oldest and best known unsolved problem in number theory. While the proof has remained elusive, the conjecture has been computer verified for numbers up to $4\\times 10^{18}$.</p>", "functions": {}, "rulesets": {}, "advice": "<p>$\\var{2a} = \\var{answers[keys(answers)[a]]}$</p>", "extensions": [], "type": "question", "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Sean Gardiner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2443/"}]}]}], "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Sean Gardiner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2443/"}]}