created 01/01/03

#
Chapter 72 Programming Exercises

## Exercise 1

A **prime number** is an integer that cannot be divided by any
integer other than one and itself.
For example, 7 is prime because its only divisors are 1 and 7.
The integer 8 is not prime because its divisors are 1, 2, 4, and 8.

Another way to define prime is:

prime(N) = prime(N, N-1)
prime(N, 1) = true
prime(N, D) = if D divides N, false
else prime(N, D-1)

For example,

prime(4) = prime(4,3)
prime(4,3) = prime(4,2)
prime(4,2) = false

Another example,

prime(7) = prime(7,6)
prime(7,6) = prime(7,5)
prime(7,5) = prime(7,4)
prime(7,4) = prime(7,3)
prime(7,3) = prime(7,2)
prime(7,1) = true

Translate the math-like definition of prime into two Java methods that
return `boolean`

.
Use the `%`

operator to test divisibility.
Put your method into a class, write a testing class, and test your
program.
(Look at `FactorialTester.java`

in this chapter.)

If you run your program for integers larger than about 12,000 (on a Windows system)
you will run out of memory.
Your program will stop running and report a *StackOverflowError*.
This is because each activation in the activation chain requires some memory,
and 12,000 activations uses up all the memory that has been reserved for this use.

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## Exercise 2

Assume that female rabbits live for only 4 months.
Modify the math-like definition of the Fibonacci series to
account for dying rabbits.
Implement the new series as a Java method.

First draw a chart showing the population of rabbits by month.
Then deduce the new rules for the series.
You will have more base cases than in the original series.

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**End of Exercises**