What's your favorite number?

My favorite number is: $3435$ . 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 $1$ ) which have the following property: $\begin{aligned}\color{#3D99F6}3\color{#D61F06}4\color{#20A900}35&=\color{#3D99F6}3^{\color{#3D99F6}3}+\color{#D61F06}4^{\color{#D61F06}4}+\color{#20A900}3^{\color{#20A900}3}+5^5\\&= \color{#3D99F6}{27}+\color{#D61F06}{256}+\color{#20A900}{27}+3125\\ &={3435}.\end{aligned}$ I also like Mills' constant which is the smallest number $\rm A$ such that $\lfloor \rm A^{3^n} \rfloor$ is a prime number for every $n\in\mathbb N$ . Its value is approximately equal to $1.306$ and the primes generated by Mills' constant are known as Mills primes; if the Riemann hypothesis is true, the sequence begins: $2, 11, 1361, 2521008887, \ldots$ (sequence A051254 in OEIS). And what about you? What is your favorite number, and why? Leave a comment! ;-)

#NumberTheory #Numbers #FavoriteNumber

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

$1023$ because...

In alphanumeric code, it spells my initials
$2^{10}-1$ looks nice
Contains digits 0 through 3
It was especially special on October 23, 2013
10:23 is my average bedtime

Justin Wong - 7 years, 1 month ago

73, from the Big Bang Theory

Nanayaranaraknas Vahdam - 7 years, 1 month ago

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 - 7 years, 1 month ago

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 $145=1!+4!+5!$ .

Finn Hulse - 7 years, 1 month ago

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

Sharky Kesa - 7 years, 1 month ago

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

Gmasha Hussain - 7 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$