Prime Number Program Java

Hi, it's have been long time since my latest post about Luhn Algorithm.
Today, I will show you how to create prime number program with Java.


What is prime number?
A prime number is a whole number greater than 1, whose only two whole-numberfactors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

How to check if given number X is prime or not?

This method will return true if X is prime and return false if X is not prime.
Time complexity for this algorithm are O( sqrt(X) ).

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public boolean isPrime(int x) { if(x<2) return false; if(x==2 || x==3) return true; if(x%2==0 || x%3==0) return false; for(int p=6; (p-1) * (p-1) <= x; p += 6) { if(x % (p-1) == 0 ) return false; if(x % (p+1) == 0 ) return false; } return true; }

How to generate prime number between A and B inclusive?
A must be less than or equal B.
Time complexity for this algorithm are O( range * sqrt(range) ), where range = B - A

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public List<Integer> genPrimes(int a, int b) { List<Integer> primes = new ArrayList<Integer>(); if(a<= 2) primes.add(2); if(a % 2 == 0) a++; for(int p=a; p<=b; p+=2) { if(isPrime(p)) primes.add(p); } return primes; }

If you want faster algorithm, please check my other post:

• Generate Prime Number With Dynamic Programming
• Prime Number With Sieve Algorithm (C++)
• Sieve With Optimized Memory (Java)

Feel free to add your question or comment. 
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