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Considering on the linked question I was the only upvoter versus six downvoters, I don't expect this answer to go down very well; but maybe someone will agree with me :-). In any case, this is how I respond, and my justification...

I always like to see these questions, and have upvoted them before. I find it quite interesting to see where elementary proof methods fail (maybe it is just me!), and these questions serve as a way to show future visitors exactly that. But the crux of the matter is that this site welcomes those who study mathematics, and if a post helps someone (anyone) learn, it is in my opinion on-topic. I will quote the help center (my boldface):

Mathematics Stack Exchange is for people studying mathematics at any level and professionals in related fields. We welcome questions about:

 
  • Understanding mathematical concepts and theorems.

Seeing where elementary methods fail can shed light on some theorems and help with understanding the mathematics behind it. Moreover, if someone believes they have solved an open problem (working on the assumption that they are wrong) then they are not understanding some concept correctly somewhere. By pointing out the error we have aided their understanding of any related topics, as well as anyone else who visits the page with the same question in the future. That is (unless I am misinterpreting the Help Center) exactly the kind of question Math.SE welcomes.

As for voting on the questions, which I understand is subjective, the linked question

  • shows research effort (doesn't look like a 5-minute-job to me!),
  • is clear (lovely formatting), and
  • is useful (that is, to anyone who (say) recreationally tries to solve this conjecture with the same elementary methods).

More generally, a good quality [proof-verification] question is not synonymous with a correct proof. This tag is not described in that way. If the situation was someone answering their own question "Are there infinitely many twin-primes?" with a false proof, then I would agree that down votes are justified, but that is not the situation here.

Considering on the linked question I was the only upvoter versus six downvoters, I don't expect this answer to go down very well; but maybe someone will agree with me :-). In any case, this is how I respond, and my justification...

I always like to see these questions, and have upvoted them before. I find it quite interesting to see where elementary proof methods fail (maybe it is just me!), and these questions serve as a way to show future visitors exactly that. But the crux of the matter is that this site welcomes those who study mathematics, and if a post helps someone (anyone) learn, it is in my opinion on-topic. I will quote the help center (my boldface):

Mathematics Stack Exchange is for people studying mathematics at any level and professionals in related fields. We welcome questions about:

 
  • Understanding mathematical concepts and theorems.

Seeing where elementary methods fail can shed light on some theorems and help with understanding the mathematics behind it. Moreover, if someone believes they have solved an open problem (working on the assumption that they are wrong) then they are not understanding some concept correctly somewhere. By pointing out the error we have aided their understanding of any related topics, as well as anyone else who visits the page with the same question in the future. That is (unless I am misinterpreting the Help Center) exactly the kind of question Math.SE welcomes.

As for voting on the questions, which I understand is subjective, the linked question

  • shows research effort (doesn't look like a 5-minute-job to me!),
  • is clear (lovely formatting), and
  • is useful (that is, to anyone who (say) recreationally tries to solve this conjecture with the same elementary methods).

More generally, a good quality [proof-verification] question is not synonymous with a correct proof. This tag is not described in that way. If the situation was someone answering their own question "Are there infinitely many twin-primes?" with a false proof, then I would agree that down votes are justified, but that is not the situation here.

Considering on the linked question I was the only upvoter versus six downvoters, I don't expect this answer to go down very well; but maybe someone will agree with me :-). In any case, this is how I respond, and my justification...

I always like to see these questions, and have upvoted them before. I find it quite interesting to see where elementary proof methods fail (maybe it is just me!), and these questions serve as a way to show future visitors exactly that. But the crux of the matter is that this site welcomes those who study mathematics, and if a post helps someone (anyone) learn, it is in my opinion on-topic. I will quote the help center (my boldface):

Mathematics Stack Exchange is for people studying mathematics at any level and professionals in related fields. We welcome questions about:

  • Understanding mathematical concepts and theorems.

Seeing where elementary methods fail can shed light on some theorems and help with understanding the mathematics behind it. Moreover, if someone believes they have solved an open problem (working on the assumption that they are wrong) then they are not understanding some concept correctly somewhere. By pointing out the error we have aided their understanding of any related topics, as well as anyone else who visits the page with the same question in the future. That is (unless I am misinterpreting the Help Center) exactly the kind of question Math.SE welcomes.

As for voting on the questions, which I understand is subjective, the linked question

  • shows research effort (doesn't look like a 5-minute-job to me!),
  • is clear (lovely formatting), and
  • is useful (that is, to anyone who (say) recreationally tries to solve this conjecture with the same elementary methods).

More generally, a good quality [proof-verification] question is not synonymous with a correct proof. This tag is not described in that way. If the situation was someone answering their own question "Are there infinitely many twin-primes?" with a false proof, then I would agree that down votes are justified, but that is not the situation here.

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Szmagpie
Szmagpie
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Considering on the linked question I was the only upvoter versus six downvoters, I don't expect this answer to go down very well; but maybe someone will agree with me :-). In any case, this is how I respond, and my justification...

I always like to see these questions, and have upvoted them before. I find it quite interesting to see where elementary proof methods fail (maybe it is just me!), and these questions serve as a way to show future visitors exactly that. But the crux of the matter is that this site welcomes those who study mathematics, and if a post helps someone (anyone) learn, it is in my opinion on-topic. I will quote the help center (my boldface):

Mathematics Stack Exchange is for people studying mathematics at any level and professionals in related fields. We welcome questions about:

  • Understanding mathematical concepts and theorems.

Seeing where elementary methods fail can shed light on some theorems and help with understanding the mathematics behind it. Moreover, if someone believes they have solved an open problem (working on the assumption that they are wrong) then they are not understanding some concept correctly somewhere. By pointing out the error we have aided their understanding of any related topics, as well as anyone else who visits the page with the same question in the future. That is (unless I am misinterpreting the Help Center) exactly the kind of question Math.SE welcomes.

As for voting on the questions, which I understand is subjective, the linked question

  • shows research effort (doesn't look like a 5-minute-job to me!),
  • is clear (lovely formatting), and
  • is useful (that is, to anyone who (say) recreationally tries to solve this conjecture with the same elementary methods).

More generally, a good quality [proof-verification] question is not synonymous with a correct proof. This tag is not described in that way. If the situation was someone answering their own question "Are there infinitely many twin-primes?" with a false proof, then I would agree that down votes are justified, but that is not the situation here.