This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .

Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.

Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold

- bulleted - list

bulleted

list

1. numbered 2. list

numbered

list

Note: you must add a full line of space before and after lists for them to show up correctly

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.

@Sharky Kesa
–
Zhang Yitang has proved a weakened form of the Twin Prime conjecture, namely that there exists an N such that there are infinitely many pairs of consecutive primes with difference < N.

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

The conjecture that the distribution of twin primes satisfies a Riemann Hypothesis type error term is well supported empirically, but I think this might be a problem that survives the current millennium.

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

Here's my explanation,

First take prime numbers ending with $1$,

you can find that there can be many triplets satisfying the condition. For example: $\boxed{ 11, 13, 17}$, $\boxed{41,43,47}$, $\boxed{101,103,107}$ etc. . .

Now, let's take primes ending with $2$,

As there is only one possibility, but that proves to be wrong. $\boxed{2,4,8}$

Now, let's take primes ending with $3$,

We can say there's only no such possibility, because the second number i.e. $n+2$ yields us a number divisible by $5$. Even this triplet proves wrong, $\boxed{3,5,9}$ as $9$ is not prime.

Now let's take primes ending with $5$,

Only one possibility, i.e. $\boxed{5,7,11}$. In all other triplets, the first number i.e. $n$ is not prime

Now, let's take primes ending with $7$,

You can find that the can be many possibilities. For example: $\boxed{ 17, 19, 23}$, $\boxed{107,109,113}$, $\boxed{227,229,233}$ etc. . .

Now, let's take primes ending with $9$,

No such possibility, because the third number i.e. $n+6$ yields us a number divisivisible by $5$

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in`\(`

...`\)`

or`\[`

...`\]`

to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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

Log in to reply

My 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

Yeah , I also think that.Thanks!

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

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

Here's my explanation,

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

197+6=203

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