/// <summary>
/// Finds the largest prime factor of num
/// </summary>
/// <param name="num">Number to find the largest prime factor for</param>
/// <returns>Largest prime factor of num or 0 if none found</returns>
public static long LargestPrimeFactor(long num)
{
if (num <= 1)
{
return(0);
}
else if (num == 2)
{
return(2);
}
else
{
long largest = 0;
long sqrtNum = (long)Math.Ceiling(Math.Sqrt((double)num));
// Check all odd numbers if they're a factor -and- they're a prime number
for (long i = 3; i <= sqrtNum; i += 2)
{
if ((num % i == 0) && Mathx.IsPrime(i))
{
largest = i;
}
}
// Check if num itself is a prime number (by definition, it's already a factor of itself)
if (Mathx.IsPrime(num))
{
largest = num;
}
return(largest);
}
}
/// <summary>
/// Get the nth prime number
/// </summary>
/// <example>
/// By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
/// </example>
/// <param name="n">Sequence number of primes</param>
/// <returns>nth prime or -1 if we're out of bounds</returns>
public static long NthPrime(int n)
{
int numPrimes = 0;
long num = 2;
while ((numPrimes < n) && (num < long.MaxValue))
{
if (Mathx.IsPrime(num))
{
numPrimes++;
}
if (numPrimes == n)
{
return(num);
}
num++;
}
return(-1);
}