What does P|a means?

Question

In the proof for the existence of unlimited prime numbers, i saw the following

let n be the number of prime numbers as P1,P2,P3,.......Pn
let a = P1P2P3....Pn+1
a > Pn and a is not a prime number
a should have a prime factor
let P be it
P|a ----> 1
but P|a-1 ----->2
1 & 2 -> P|1
but 1 doesn't have a factor ........
and the proof follows

but i didn't understand the symbol P|a
what does P|a means? please somebody explain me

Answer 1

It means $P$ is a divisor of $a$.

Answer 2

P|a means P divides a.For P|a we can also write this as Pc=a where c is a constant.It simply means that $$P*c=a$$ or P is a factor of a.

Answer 3

It means $p$ is a divisor of $a$, i.e $a$ leaves a remainder of $0$ when divided by $p$. You can also write $a \equiv 0 \text{ mod }p$.