{"status": "success", "data": {"description_md": "Goldbach's conjecture states that every even integer greater than 2 can be written as the sum of two prime numbers (for example, $2016=13+2003$). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of?\n\n$\\textbf{(A)}\\ \\text{an odd integer greater than } 2 \\text{ that can be written as the sum of two prime numbers}$<br> $\\textbf{(B)}\\ \\text{an odd integer greater than } 2 \\text{ that cannot be written as the sum of two prime numbers}$ <br>$\\textbf{(C)}\\ \\text{an even integer greater than } 2 \\text{ that can be written as the sum of two numbers that are not prime}$<br> $\\textbf{(D)}\\ \\text{an even integer greater than } 2 \\text{ that can be written as the sum of two prime numbers}$ <br>$\\textbf{(E)}\\ \\text{an even integer greater than } 2 \\text{ that cannot be written as the sum of two prime numbers}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Goldbach&#8217;s conjecture states that every even integer greater than 2 can be written as the sum of two prime numbers (for example, <span class=\"katex--inline\">2016=13+2003</span>). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\text{an odd integer greater than } 2 \\text{ that can be written as the sum of two prime numbers}</span><br/> <span class=\"katex--inline\">\\textbf{(B)}\\ \\text{an odd integer greater than } 2 \\text{ that cannot be written as the sum of two prime numbers}</span> <br/><span class=\"katex--inline\">\\textbf{(C)}\\ \\text{an even integer greater than } 2 \\text{ that can be written as the sum of two numbers that are not prime}</span><br/> <span class=\"katex--inline\">\\textbf{(D)}\\ \\text{an even integer greater than } 2 \\text{ that can be written as the sum of two prime numbers}</span> <br/><span class=\"katex--inline\">\\textbf{(E)}\\ \\text{an even integer greater than } 2 \\text{ that cannot be written as the sum of two prime numbers}</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2016 AMC 12A Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p06", "prev": "/problem/16_amc12A_p04"}}