What's your favorite (positive integer) number?
Realistically; no keyboard-smash number strings.
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zsvdkhnorc
I'm fond of most powers of two.
TetrisGuy · 26-30, M
I am most fond of Fibonacci numbers, then powers of two. Oddly enough, 8 is my least favorite number, even though it satisfies both criteria of being a power of two and a Fibonacci number. It makes me wonder things about how 2³ and 12² happen to be the only two known Fibonacci numbers that do not introduce a new prime.
TheFurryOat
What do you even mean by "8 and 144 are the only Fibonacci numbers that don't introduce a new prime"?
TetrisGuy · 26-30, M
As far as we have seen, the prime factorizations of every Fibonacci number has introduced a new prime factor... except 8 and 144.
TheFurryOat
Prime factorizations? Just write "Carmichaels theorem says that {1,8,144} are the only Fibonacci numbers that do not have a unique prime factor";
and, I doubt it has to do with anything but the fact that 2, 8 and 144 are the 3 smallest even numbers and only 2 is prime.
and, I doubt it has to do with anything but the fact that 2, 8 and 144 are the 3 smallest even numbers and only 2 is prime.
TheFurryOat
scratch that, 2 and 8 the smallest even numbers.
TetrisGuy · 26-30, M
I think it has to do with the fact 8 is 2³ and 144 is 12².