A prime number is a number that has only two divisors, 1 and the number itself. To find the largest prime smaller than a given number you should first write a function that determines if a number is prime and then call this function, starting from the given number, towards 1 until the first prime is encountered. There are various algorithms for determining if a number is prime. Common implementations for determining the primality appear as follows:
bool is_prime(int const num)
{
if (num <= 3) { return num > 1; }
else if (num % 2 == 0 || num % 3 == 0)
{
return false;
}
else
{
for (int i = 5; i * i <= num; i += 6)
{
if (num % i == 0 || num % (i + 2) == 0)
{
return false;
}
}
return true;
}
}
This function can be used as follows:
int main()
{
int limit = 0;
std::cout << "Upper limit:";
std::cin >> limit;
for (int i = limit; i > 1; i--)
{
if (is_prime(i))
{
std::cout << "Largest prime:" << i << std::endl;
return 0;
}
}
}