Prime numbers have fascinated professional and amateur mathematicians alike since ancient times. It's a simple concept—a *prime* number is any integer greater than 1 that is divisible only by 1 and itself. An integer greater than 1 that is not prime is *composite.* In this chapter, we'll use Java to explore two topics related to prime numbers.

The first topic is *primality testing.* Given a positive integer, how can we tell whether it is prime or composite? Of course, we can systematically try dividing the number by a succession of “trial divisors”—if we find a divisor other than 1 and the number itself that divides evenly into the number (the division leaves no remainder), then the number is composite. If we fail to find such ...

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