what is the probability that a prime number divides another prime plus 1?
what I do know is that for 2 it's 100%
I can show this fact using a function
$f(x,y):=$ the number of primes between $1$ & $y$ that when you add 1 you can divide it by $prime(x)$ and get a whole number and divide that by $π(y)$
$π(x)$ is the prime counting function
$f(1,x)=(π(x)-1)/π(x)$ because the only time $prime(x)+1$ doesn't equal an even number is when the prime is $2$.
$2+1$ isn't even.
and as the x goes to infinity $(π(x)-1)/π(x)$ goes to 100%
my question is what is the probability that $3,5,7,...$ divides a random prime number plus 1
do you know the general formula for $f(x,y)$ as $y$ goes to infinity