Solving Project Euler Problem 7: The 10001st Prime Number

 Problem

By listing the first six prime numbers: 2, 3, 5, 7, 11 and 13, we can see that the 6^th prime is 13.  What is the 10 001^st prime number?

 Solution

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that cannot be evenly divided by any other number except 1 and itself.

For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13. These numbers cannot be divided by any other integer except 1 and themselves, making them prime.

 

 

1.      We define a helper function, prime, which takes an integer n as input and checks if it is prime. The function first handles special cases (1 and 2) and then uses a common optimization for prime checking, which involves checking divisibility only up to the square root of n.

2.      The find_10001st_prime function is responsible for finding the 10,001st prime number. It initializes count to 0 and number to 2.

3.      The while loop continues indefinitely until we find the 10,001st prime number.

4.      Inside the loop, we use the prime function to check if number is prime. If it is, we increment the count by 1.

5.      If count reaches 10,001, we break out of the loop because we have found the desired prime number.

6.      Otherwise, if number is not prime, we increment it by 1 and continue the loop to check the next number.

7.      After the loop finishes, the value of number will be the 10,001st prime number.

 

Solving Project Euler Problems provides a great opportunity to practice coding and algorithmic thinking.