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!

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

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

Log in to reply

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

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

Log in to reply

Yeah , I also think that.Thanks!

Log in to reply

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

Log in to reply

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

Here's my explanation,

Log in to reply

197+6=203

Log in to reply

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

Log in to reply

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

Log in to reply

Lol Btw Nice observation.

Log in to reply

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

pic

Log in to reply

Ah! Those were deleted by me :P

Log in to reply

Log in to reply

Log in to reply