I happened to see this problem. So I came up with a similar problem below.

How many integers \(n>1\) are there such that \(n,n+2,n+6\) are all prime numbers ?

Do post Awesome solutions with proofs!

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## Comments

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TopNewestMy intuition says there are infinitely many such \(n\).

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If there are infinitely many such n, then the twin prime conjecture is true. I suggest working on the twin prime conjecture first, because it is (likely) easier.

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Has anyone come close to proving the twin prime conjecture or do we need to solve the Riemann hypothesis first?

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Here is a good introductory read to the relationships between TP and RH. It is written by Dan Goldston (same as the above), though prior to Zhang's discovery. If you can understand through the first 5 chapters, that would be great

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Yeah , I also think that.Thanks!

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@Kalpok Guha @Otto Bretscher @Calvin Lin @Pi Han Goh

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Yes, even as I was working out I found many numbers,

Here's my explanation,

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197+6=203

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I didn't know 71+6=79. :P

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@Sravanth Chebrolu I think you must develop a habit of always cross checking your work. :)

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Lol Btw Nice observation.

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Where did you comment the 3 comments? I can only see one here.

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Ah! Those were deleted by me :P

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