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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, 8 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
· 2 years, 8 months ago

4, because I used to think that numbers had personalities. 4 is kind. · 2 years, 7 months ago

1. My family literally revolves around 5 and any number who's ultimate digit sum is 5.
· 2 years, 8 months 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 $$145=1!+4!+5!$$. · 2 years, 8 months 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... · 2 years, 8 months ago