!rant
... so... maybe not that much of a thing, but i think it is:

a gal (27 years old) i started teaching programming two weeks ago, who had literally no previous experience with programming, algoritmization nor c#...
... just now, after 3 lessons of 6 hours altogether, and after yesterday when i explained to her what arrays are and reminded her what loops do...

... invented bubble sort. on her own. no googling. on paper. no "trial and error code typing and running".

i'm actually pretty proud of her :)

... putting the algo concept into actual code will still be a bit of a struggle, but yeah, hell, can't help thinking that she's actually pretty smart :)

(p. s. fist lesson was i drew uml of a fibonacci algo and forced her to understand what it does, second lesson was i explained the minimum required c# syntax for her to be able to implement it and forced her to write it (with as little help as i could), third lesson was the concept of array and "okay, now here's array of numbers, make a function that will sort them")

looking forward to what will happen when i explain recursion and nudge her towards quicksort O:-)

Maybe I'm severely misunderstanding set theory. Hear me out though.

Let f equal the set of all fibonacci numbers, and p equal the set of all primes.

If the density of primes is a function of the number of *multiples* of all primes under n,
then the *number of primes* or density should shrink as n increases, at an ever increasing rate
greater than the density of the number of fibonacci numbers below n.

That means as n grows, the relative density of f to p should grow as well.
At sufficiently large n, the density of p is zero (prime number theorem), not just absolutely, but relative to f as well. The density of f is therefore an upper limit of the density of p.

And the density of p given some sufficiently large n, is therefore also a lower limit on the density of f.

And that therefore the density of p must also be the upper limit on the density of the subset of primes that are Fibonacci numbers.

WHICH MEANS at sufficiently large values of n, there are either NO Fibonacci primes (the functions diverge), and therefore the set of Fibonacci primes is *finite*, OR the density of primes given n in the prime number theorem
*never* truly reaches zero, meaning the primes are in fact infinite.

Proving the Fibonacci primes are infinite, therefore would prove that the prime number line ends (fat chance). While proving the primes are infinite, proves the Fibonacci primes are finite in quantity.

And because the number of primes has been proven time and again to be infinite, as far back as 300BC,the Fibonacci primes MUST be finite.

QED.

If I've made a mistake, I'd like to know.