By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
Q: What is the 10001st prime number?
Train of thought
- The even numbers is definitely not prime number. (expect 2)
- Among odd numbers, using all multiply self of odd numbers that are less than an odd number as prime factors to judge whether this odd number is prime number
Solutions
public static void main(String[] args) {
// calculate the quantity of prime numbers
int count = 1;
// only check odd numbers, expect 2
int num = 3;
// stop when count = 10001, return result
while (count < 10001) {
if (isPrime(num)) {
count++;
}
num += 2;
}
// result should minus the 2 added above
System.out.println(num - 2);
}
public static boolean isPrime(int num) {
if (num <= 2) {
return true;
}
if (num % 2 == 0) {
return false;
}
// using all multiply self of odd numbers less than and equal an odd number to judge the prime number
for (int i = 3; i * i <= num; i += 2) {
if (num % i == 0) {
return false;
}
}
return true;
}
The complexity
Time complexity: O(n²)
