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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
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Open problems with monetary rewards
Recently, I have offered 100 € cash prize for a proof of the conjectured primality test which is formulated in this post.