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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: \[\begin{align}\color{blue}3\color{red}4\color{green}35&=\color{blue}3^{\color{blue}3}+\color{red}4^{\color{red}4}+\color{green}3^{\color{green}3}+5^5\\&= \color{blue}{27}+\color{red}{256}+\color{green}{27}+3125\\ &={3435}.\end{align}\] 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! ;-)

Note by حكيم الفيلسوف الضائع
2 years, 5 months ago

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\(1023\) 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 · 2 years, 5 months ago

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4, because I used to think that numbers had personalities. 4 is kind. Gmasha Hussain · 2 years, 4 months ago

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  1. My family literally revolves around 5 and any number who's ultimate digit sum is 5.
Sharky Kesa · 2 years, 5 months ago

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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 · 2 years, 5 months ago

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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 · 2 years, 5 months ago

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73, from the Big Bang Theory Nanayaranaraknas Vahdam · 2 years, 5 months ago

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