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!

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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TopNewestMy intuition says there are infinitely many such \(n\). – Nihar Mahajan · 2 years, 1 month ago

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– Calvin Lin Staff · 2 years, 1 month ago

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.Log in to reply

– Sharky Kesa · 2 years, 1 month ago

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

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

– Calvin Lin Staff · 2 years, 1 month agoLog in to reply

– Nihar Mahajan · 2 years, 1 month ago

Yeah , I also think that.Thanks!Log in to reply

@Kalpok Guha @Otto Bretscher @Calvin Lin @Pi Han Goh – Nihar Mahajan · 2 years, 1 month ago

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

Here's my explanation,

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– Aditya Chauhan · 2 years, 1 month ago

197+6=203Log in to reply

– Sharky Kesa · 2 years, 1 month ago

I didn't know 71+6=79. :PLog in to reply

@Sravanth Chebrolu I think you must develop a habit of always cross checking your work. :) – Nihar Mahajan · 2 years, 1 month ago

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– Aditya Chauhan · 2 years, 1 month ago

Lol Btw Nice observation.Log in to reply

pic

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– Sravanth Chebrolu · 2 years, 1 month ago

Ah! Those were deleted by me :PLog in to reply

– Aditya Chauhan · 2 years, 1 month ago

I guess U r the fastest one to get 200k points. Keep solving and making more problems.Log in to reply

– Sravanth Chebrolu · 2 years, 1 month ago

Thanks! I'll be posting a new set keep your eyes on that!Log in to reply