Are there infinite primes? If yes, or no, could you prove it? Any useful internet resources?

Is there a usual pattern for primes?

How to define Mersenne primes? ( \( M_n=2^n-1) \). And how many of them had been found?

And others? Like Wilson's Theorem \( (n-1)! \equiv -1 (\text{mod n}) \)? Or all coefficients of \( (x-1)^y -(y^p)-1 \) is divisible by \( y \), then \( y \) must be prime.

Recently, I knew that the largest known prime number, which is discovered in August \( 2015 \) by Great Internet Mersenne Prime Search, is \[ \displaystyle \Huge{ \color{green}{2}^{\color{blue}{57,885,161}} - \color{red}{1}} \]It contains \( 17, 425,170 \) digits! It's a Mersene prime.

Also, the largest non-Mersenne prime number is:

\[ \Huge \color{green}{19249} \color{red}{\times 2^{\color{blue}{13018586}}} + 1 \]

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*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:

TopNewestI was excited to hear they had discovered a new larger Mersenne prime. Then I read closer and found that this is the largest known prime so far as of this month.

It was actually discovered back in 2013. Seems like it's past time they found a bigger one, right?

Log in to reply

Nope, there is no pattern to primes, in the sense that there's no simple formula that we can plug numbers into to calculate the nth prime.

However, there are some cool patterns relating to the distribution of primes among the integers. I vaguely remember a nice YouTube video about that: I'll link it here if I can find it...

Log in to reply

Yes there are infinite primes. There are some proofs in the brilliant wikis and obviously on the wikipedia too. Here is a link-- Infinitely Many Primes

Log in to reply

FYI, you can use our nifty wiki linking tool to easily link to wiki pages

Log in to reply

Infinitely Many Primes

understood. Thanks.

Log in to reply