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CMPS 12A
Introduction to Programming
Winter 2008
Programming Assignment 4
Due Tuesday February 19, 10:00 pm
In this project you will write a Java program that reads a positive integer from standard input, then
determines whether or not that number is prime. We say that an integer n is divisible by a non-zero
integer d if there exists an integer k such that n  k  d , i.e. if d divides evenly into n. We also say in this
context that d is a divisor of n. Recall that a positive integer n is called prime if its only positive divisors
are 1 and n. The one exception to this rule is the number 1 itself, which is considered to be non-prime. A
positive integer that is not prime is called composite. Euclid showed that there are infinitely many prime
numbers. The prime and composite sequences begin as follows:
Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …
Composites: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, …
There are many ways to test a number for primality, but perhaps the simplest is to just do trial divisions.
Begin by dividing n by 2, and if it divides evenly, then n is not prime. Otherwise, divide by 3, then 4,
then 5, etc. If at any point n is found to be divisible by a number d in the range 2  d  n  1, then halt,
and conclude that n is composite. Otherwise, conclude that n is prime. Actually, a moments thought
reveals that is not necessary to go all the way up to n  1 . One need only do trial divisions of n by
integers d in the range 2  d  n . (To see this, suppose n  1 is composite. Then there exist positive
integers a and b such that 1  a  n , 1  b  n , and n  a  b . But if both a  n and b  n , then
a  b  n , contradicting that n  a  b . Hence one of a or b must be less than or equal to n .)
You can implement this procedure in Java by writing a loop controlled by an int variable d, which starts
at d  2 , and halts when either a trial division by d succeeds, or when d 2  n . It may be useful to declare
a variable of type boolean called isPrime which is initialized to true, and whose value is recalculated
on each iteration of the loop. isPrime can then be used as part of the loop repetition condition. To
perform a trial division by d, one need only calculate the remainder of n upon division by d, and compare
that remainder to zero. Recall that the remainder is given by the Java expression n%d. (For more on the
integer division operation, see the pa3 project description.)
Just as in pa3, your program will carry out a robust interaction with the user to check for correct input. In
particular, if the user enters anything other a positive integer, your program will continue to prompt for
more input. You must design appropriate loops to carry out these checks. It may be useful to study the
program CheckInput2.java on the webpage to see how to do this. Format your program output to
coincide with the sample runs below.
% java Prime
Enter a positive integer: 25.6
Please enter a positive integer: -15
Please enter a positive integer: xyz
Please enter a positive integer: 73
73 is prime
1
% java Prime
Enter a positive integer: 252525
252525 is composite
% java Prime
Enter a positive integer: 764321
764321 is prime
% java Prime
Enter a positive integer: 1
1 is composite
Observe that non-positive integers, double values, and non-numeric strings are rejected until a positive
integer is entered. It is recommended that you first write a program that does no input checking of any
kind, and just determines the primality of a positive integer correctly. When this is done, implement the
input checks described above.
What to turn in
Name your source file for this project Prime.java and submit it to the assignment name pa4 in the
usual way:
% submit cmps012a-pt.w08 pa4 Prime.java
Use peek to check that submit was successful, then double check manually by following the instructions
in pa1 and lab1.
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