What's your favorite number?

My favorite number is: 34353435. You may ask: "why?" since this number seems, à priori, pretty boring. But it turns out that it is very interesting: it is the only natural number (along with 11 ) which have the following property: 3435=33+44+33+55=27+256+27+3125=3435.\begin{aligned}\color{#3D99F6}3\color{#D61F06}4\color{#20A900}35&=\color{#3D99F6}3^{\color{#3D99F6}3}+\color{#D61F06}4^{\color{#D61F06}4}+\color{#20A900}3^{\color{#20A900}3}+5^5\\&= \color{#3D99F6}{27}+\color{#D61F06}{256}+\color{#20A900}{27}+3125\\ &={3435}.\end{aligned} I also like Mills' constant which is the smallest number A\rm A such that A3n\lfloor \rm A^{3^n} \rfloor is a prime number for every nNn\in\mathbb N. Its value is approximately equal to 1.3061.306 and the primes generated by Mills' constant are known as Mills primes; if the Riemann hypothesis is true, the sequence begins: 2,11,1361,2521008887,2, 11, 1361, 2521008887, \ldots (sequence A051254 in OEIS). And what about you? What is your favorite number, and why? Leave a comment! ;-)

Note by حكيم الفيلسوف الضائع
5 years, 6 months ago

No vote yet
1 vote

  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:

  • 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.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

10231023 because...

  • In alphanumeric code, it spells my initials
  • 21012^{10}-1 looks nice
  • Contains digits 0 through 3
  • It was especially special on October 23, 2013
  • 10:23 is my average bedtime

Justin Wong - 5 years, 6 months ago

Log in to reply

73, from the Big Bang Theory

Nanayaranaraknas Vahdam - 5 years, 6 months ago

Log in to reply

8... because in a digital clock all the digits and also the letters can be formed by 8.. for example- to form 3 in a digital clock we just have to take out the two sticks on the left...

Divyansh Rai - 5 years, 6 months ago

Log in to reply

I was born on the fifth hour of the fifth day of the fifth month of the year on the fifth floor of the hospital, and I used to be 5 years old. That's why my favorite number is 145=1!+4!+5!145=1!+4!+5!.

Finn Hulse - 5 years, 6 months ago

Log in to reply

  1. My family literally revolves around 5 and any number who's ultimate digit sum is 5.

Sharky Kesa - 5 years, 6 months ago

Log in to reply

4, because I used to think that numbers had personalities. 4 is kind.

Gmasha Hussain - 5 years, 5 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...