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
7 years, 1 month ago

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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 - 7 years, 1 month ago

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73, from the Big Bang Theory

Nanayaranaraknas Vahdam - 7 years, 1 month 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 - 7 years, 1 month 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!145=1!+4!+5!.

Finn Hulse - 7 years, 1 month ago

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

Sharky Kesa - 7 years, 1 month ago

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

Gmasha Hussain - 7 years ago

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