Checkpoint B

Number Theory

We are writing a bunch of number-related functions. Even though many of them have nothing to do with prime numbers, the class is called Prime.

Fields

• int nprimes
• Array primes

Accessor methods

• method int getNPrimes(): How many primes are in the array? This should be stored in the nprimes variable.
• method int getPrime(int k): Get the kth prime, starting with getPrime(0) = 2.

Functions

• function boolean divides(int k, int n): True when k divides n.
• function int isqrt(n): Returns the greatest integer k with k*k <= n.
• function int countDivisors(int n): Returns the number of divisors of n. countDivisors(7) = 2.
• function Array divisors(int k): An Array containing the divisors of k in ascending order.

More Methods

• constructor Prime new(int k): Create a Prime object. The object should contain:
  1. an integer: the number of primes found (this will be k);
  2. an array of integers that is filled with the first k prime numbers. When k=2 the array contains only the numbers 2 and 3.
• method boolean isKnownComposite(int n): True when the number is divisible by some number in the primes list, but is not itself prime.

Testing

• Main.jack testing code.

class Prime {
  field int nprimes
  field Array primes;

  method int getNPrimes() { return nprimes; }
  method int getPrime(int k) { return primes[k]; }
  // ...
}

Common Issues

• Constructors need to return this.