วีดีโอ

999999999999999999999999999999999999999999999999999999999999999

At least bacon is good

Another day another fricken story

the slender girl say 99999999999999999999999999999999999999999999999999999999999999999999999 but its sound like she say it nyan im from poland i dont speak good english

0:47 NAAH I THINK ILL WATCH!!!!

0:48 i just LOVE the font!!!

Tra tra tra tra tra tra tra

AhAhAhAhAh

Hahaha to hahaha haha to hahaha to yo haha

Xiao Ling says this happends to me to

Please part 4 but i wanna be in the story 4 pleasee i beg you and put me if i was speaking spanish

Please part 4 but i wanna be in the story 4 pleasee i beg you and put me if i was speaking spanish

This kinda like a movie! it’s so good!

bacon is better than slender

Best Roblox story I watched 100000000000/10

^_^

0:50 bros him

0:02 sigma bacon dance

0:01 sigma bacon dance

2:48

Can you Add me afz_prepose90

“And to make the viewers happy” (SMACK) AAAAAAHHHHHHHHHHHH

SPEAR OF JUSTICE OMG 0:36

2:08 "trastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastrastras-" 🗣️🗣️🗣️🗣️🔥🔥🔥🔥🔥🔥

2:48 second skip

im kind of pissed off because of the characters blocking the entire ass screen. can you make them a bit smaller?

Can I be in part five (Yessir_withmike)

THAT start GOT ME😭

Idea: if they say I have negative money say GET OUT ( I wish I can get added to a vid ) For part 3 :D

The Riemann Hypothesis is indeed a fascinating and profound conjecture in mathematics with deep implications for number theory, particularly concerning the distribution of prime numbers. Let's break down some of the key elements in more detail. ### The Riemann Hypothesis The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function, \(\zeta(s)\), lie on the critical line in the complex plane, \(\Re(s) = \frac{1}{2}\). These zeros are of the form \(s = \frac{1}{2} + it\), where \(t\) is a real number. ### The Riemann Zeta Function The zeta function \(\zeta(s)\) is initially defined for complex numbers \(s = \sigma + it\) with \(\Re(s) > 1\) as: \[ \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} \] This series converges absolutely for \(\Re(s) > 1\). However, the zeta function can be extended to other values of \(s\) (except \(s = 1\)) through a process called analytic continuation. The function has trivial zeros at the negative even integers (\(-2, -4, -6, \ldots\)). ### Importance of the Riemann Hypothesis The hypothesis has significant implications for understanding the distribution of prime numbers. It suggests that primes are distributed as regularly as possible, given their known asymptotic density described by the Prime Number Theorem. ### Implications If the Riemann Hypothesis is true, it would lead to a more precise understanding of the error term in the Prime Number Theorem. This would refine our knowledge about the density and gaps between successive prime numbers. ### History and Status - **Proposed by Bernhard Riemann**: Riemann introduced this hypothesis in his 1859 paper, "On the Number of Primes Less Than a Given Magnitude." - **Unproven**: Despite extensive efforts by many mathematicians, no one has yet proven or disproven the hypothesis. - **Millennium Prize Problem**: It is one of the seven Millennium Prize Problems, with a reward of $1 million for a correct proof. ### Non-trivial Zeros Non-trivial zeros are the complex zeros of the zeta function that lie in the critical strip, \(0 < \Re(s) < 1\). The hypothesis claims that these zeros all have their real part equal to \(\frac{1}{2}\). ### Example Problems and Exercises 1. **Convergence of the Zeta Function's Series for \(\Re(s) > 1\)**: - The series \(\sum_{n=1}^{\infty} \frac{1}{n^s}\) converges absolutely for \(\Re(s) > 1\) because each term \(\frac{1}{n^s}\) diminishes rapidly as \(n\) increases. This can be shown by comparison to the integral test or by noting that the series resembles a p-series \(\sum \frac{1}{n^p}\) with \(p > 1\). 2. **Evaluating \(\zeta(s)\) for Simple Cases**: - For \(s = 2\), we have the well-known result: \[ \zeta(2) = \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \] - For \(s = 1\), the series diverges, leading to a pole at \(s = 1\). 3. **Understanding the Critical Strip**: - The critical strip is defined by the region \(0 < \Re(s) < 1\) in the complex plane. The Riemann Hypothesis asserts that all non-trivial zeros of \(\zeta(s)\) within this strip lie on the line \(\Re(s) = \frac{1}{2}\). These example problems help illustrate some foundational aspects of the Riemann zeta function and why the Riemann Hypothesis is such a central topic in number theory. If you have any more specific questions or need further clarification on any aspect, feel free to ask!😅

The Riemann Hypothesis is indeed a fascinating and profound conjecture in mathematics with deep implications for number theory, particularly concerning the distribution of prime numbers. Let's break down some of the key elements in more detail. ### The Riemann Hypothesis The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function, \(\zeta(s)\), lie on the critical line in the complex plane, \(\Re(s) = \frac{1}{2}\). These zeros are of the form \(s = \frac{1}{2} + it\), where \(t\) is a real number. ### The Riemann Zeta Function The zeta function \(\zeta(s)\) is initially defined for complex numbers \(s = \sigma + it\) with \(\Re(s) > 1\) as: \[ \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} \] This series converges absolutely for \(\Re(s) > 1\). However, the zeta function can be extended to other values of \(s\) (except \(s = 1\)) through a process called analytic continuation. The function has trivial zeros at the negative even integers (\(-2, -4, -6, \ldots\)). ### Importance of the Riemann Hypothesis The hypothesis has significant implications for understanding the distribution of prime numbers. It suggests that primes are distributed as regularly as possible, given their known asymptotic density described by the Prime Number Theorem. ### Implications If the Riemann Hypothesis is true, it would lead to a more precise understanding of the error term in the Prime Number Theorem. This would refine our knowledge about the density and gaps between successive prime numbers. ### History and Status - **Proposed by Bernhard Riemann**: Riemann introduced this hypothesis in his 1859 paper, "On the Number of Primes Less Than a Given Magnitude." - **Unproven**: Despite extensive efforts by many mathematicians, no one has yet proven or disproven the hypothesis. - **Millennium Prize Problem**: It is one of the seven Millennium Prize Problems, with a reward of $1 million for a correct proof. ### Non-trivial Zeros Non-trivial zeros are the complex zeros of the zeta function that lie in the critical strip, \(0 < \Re(s) < 1\). The hypothesis claims that these zeros all have their real part equal to \(\frac{1}{2}\). ### Example Problems and Exercises 1. **Convergence of the Zeta Function's Series for \(\Re(s) > 1\)**: - The series \(\sum_{n=1}^{\infty} \frac{1}{n^s}\) converges absolutely for \(\Re(s) > 1\) because each term \(\frac{1}{n^s}\) diminishes rapidly as \(n\) increases. This can be shown by comparison to the integral test or by noting that the series resembles a p-series \(\sum \frac{1}{n^p}\) with \(p > 1\). 2. **Evaluating \(\zeta(s)\) for Simple Cases**: - For \(s = 2\), we have the well-known result: \[ \zeta(2) = \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \] - For \(s = 1\), the series diverges, leading to a pole at \(s = 1\). 3. **Understanding the Critical Strip**: - The critical strip is defined by the region \(0 < \Re(s) < 1\) in the complex plane. The Riemann Hypothesis asserts that all non-trivial zeros of \(\zeta(s)\) within this strip lie on the line \(\Re(s) = \frac{1}{2}\). These example problems help illustrate some foundational aspects of the Riemann zeta function and why the Riemann Hypothesis is such a central topic in number theory. If you have any more specific questions or need further clarification on any aspect, feel free to ask!😅

4:44 intro

Im be in part 9

can i be in a story pls user: kidflash0216

I swear if you upload another video, I’m going back to fnf. By the way, thanks for adding me into this!

I swear if you upload another video, I’m going back to fnf.

2:25 germany

Wow this can make a game

new character:acorn

i have 282929292926362626383838399999 hahaha 9999999999 raw buck

2:25 najn najn najn najn

1:28 click on to get free robux

0:04 woah

I wanna be in part 4 (Ultranotpowerful)

2 sons? Hi (to the one who has a brain and the one who doing a obby)

It will mean in the world if you add me into part 4

Jsm

whats the music on the end?

1:20 OHH BOOHOO LEMME PLAY A SAD SONG ON THE WORLD’S SMALLEST VIOLIN FOR YOU!

Imma be in part 8-