My favorites

Below are my favorite numbers, Pythagoras triangle and mathematical formula.

My favorite numbers

Below, you will find my favorite numbers, ranging from 1 to 9 digits.

Digits	Number	Reason
`1`	`2`	`2 + 2 = 2 * 2` The only number for which this is true, and the only even prime.
`2`	`64`	`64 = 2⁶ = 4³ = 8²` Add 1900 to it and you have my year of birth.
`3`	`145`	`145 = 1! + 4! + 5!` The only other number for which this is true has 5 digits. See below.
`4`	`3435`	`3435 = 3³ + 4⁴ + 3³ + 5⁵` The only other number for which this is true has 9 digits. See below.
`5`	`40585`	`40585 = 4! + 0! + 5! + 8! + 5!`
`6`	`739397`	The largest prime that remains a prime when removing any number of digits from the left or right side.
`7`	`4478976`	`1679616^1679616 + 2985984^2985984 = 4478976^4478976` There are no other solutions for the formula `p^p + q^q = r^r`.
`8`	`12345679`	`12345679 * 9 = 111111111`
`9`	`438579088`	`438579088 = 4⁴ + 3³ + 8⁸ + 5⁵ + 7⁷ + 9⁹ + 0⁰ + 8⁸ + 8⁸` That is, when you define 0⁰ = 0.

And the winner is . . . 2592 = 2⁵·9²

My favorite Pythagoras triangle has sides 693, 1924 and 2045. Why? Because its area is 666666.

2002-08-12