Question

How do I calculate the largest prime number smaller than value x?

In actual fact, it doesn’t have to be exact, just approximate and close to x.

x is a 32 bit integer.

The idea is that x is a configuration parameter. I’m using the largest prime number less than x (call it y) as the parameter to a class constructor. The value y must be a prime number.

Answer 1

Some good info here on the function pi(x). Apparently,

pi(x) = the number of primes less than x

and you can approximate pi(x) with

x/(log x - 1)

while

the n-th prime of that list of primes is equal to approximately n(log n)