Finding the nth prime number can be accomplished using a function that implements the Sieve of Eratosthenes algorithm or a straightforward approach to check for primality. Below is a Python function that utilizes a basic method for generating prime numbers until it reaches the nth prime.
###### Python Function to Find the nth Prime Number

def is_prime(num):
"""Helper function to check if a number is prime."""
if num < 2:
return False
for i in range(2, int(num**0.5) + 1):
if num % i == 0:
return False
return True
def nth_prime(n):
"""Function to find the nth prime number."""
if n < 1:
raise ValueError("n must be a positive integer.")
count = 0 # To count the number of primes found
candidate = 1 # Start checking for prime from 1
while count < n:
candidate += 1 # Move to the next number
if is_prime(candidate):
count += 1 # Found a prime number
return candidate
# Example usage:
nth = 10
print(f"The {nth}th prime number is: {nth_prime(nth)}")

###### Explanation:

1. **is_prime Function**: This helper function checks if a given number is prime. It returns *False* for numbers less than 2 and checks for factors up to the square root of the number for efficiency.
2. **nth_prime Function**: This function finds the nth prime:
- It initializes a counter (*count*) to track the number of prime numbers found and a *candidate* variable starting from 1.
- A *while* loop continues until the desired *n* primes are found.
- For each candidate number, it checks if it is prime using the *is_prime* function. If it is, the counter increments.
- When the counter reaches *n*, the function returns the latest prime number found.
###### Example Usage:

Using this function, you can find any nth prime by calling *nth_prime(n)*, where *n* is a positive integer indicating which prime number to find. For instance, calling *nth_prime(10)* will return the 10th prime number.
This implementation is efficient for small values of *n*, but improvements can be made for larger values by considering more advanced algorithms like the Sieve of Eratosthenes for generating a list of prime numbers.