3: Assignment Fun with Primes
Assigned: Design Due: Program Due: Total Value: EE312 The University of Texas at Austin Spring 2008 Tuesday, February 12th Tuesday, February 19, at the beginning of class Tuesday, February 26, before midnight 20 points total (see Deliverables below for details).
Purpose Learning how to design your program before coding Learning how to write and use functions in your programs Learning about array manipulation Background The Sieve of Eratosthenes is a simple, ancient algorithm for finding all the prime numbers up to a specified integer. It was created by Eratosthenes (in 276 BC - 194 BC), a Greek mathematician, geographer and astronomer. For more information see Wikipedia http://en.wikipedia.org/wiki/Eratosthenes Deliverables There are both design (4 points) and code (16 points) deliverables for this assignment. The design portion requires that you produce these two items on paper: 1. Functional Block diagram identifying the main program and all subfunctions, showing who calls whom, and what data is passed to and from different blocks (2 points) 2. Flow chart or pseudocode of your program's main logic 1 page should be sufficient detail (2 points) Turn these in at the beginning of your Tuesday, February 19th lecture period with your name and unique section number written clearly on them. It would be a good idea (not required) to have your design reviewed by a TA in the lab before starting to write any code. The code deliverable will be submitted through the Blackboard assignment manager as usual. It will be a file named primes.c that contains all the source code and comments that meet the requirements for this assignment. Your code must also conform to the C coding standards for this course (as posted on the Blackboard for your section). Assignment Description Develop a program using the sieve algorithm below to display all n prime numbers starting from 2, where n is a value specified by the user. Prime numbers are represented in integer format. The user will be asked to input a number n. The program will then display n primes starting from 2. In your program, prime numbers are to be stored in the short int type. If the size of the largest prime number to be displayed exceeds the capacity of the system, then the program should give the longest series of primes that can be displayed and state that a further list of prime numbers cannot be generated. After displaying the complete list of n prime numbers, the program will find and output those prime numbers in the range which have additional Page 1 of 3
Assignment 3: Fun with Primes
EE312 The University of Texas at Austin Spring 2008 characteristics as defined below. Your program should allow the user to do the above for additional input values, by prompting the user and accepting a `Y' or `N' character to determine whether to repeat or not. Input requirements The user is asked to input a number n (an integer) which represents the number of prime numbers to be displayed. The program should determine whether the input value is valid (based on the value ranges of integer types on the particular machine). In this case, the input value is invalid if the nth prime number is too large for the system. Your program does not have to disallow an invalid input; instead, it should handle the invalid integer input as discussed in the assignment description. The only other valid (non-integer) inputs are `Y' and `N', which the inputs user when queried after the programs' output. Any other non-integer input should cause the program to reprompt the user for the correct input. Output requirements Display the final set of prime numbers in an 8 column, table format. The prime numbers must be in ascending order with the lowest prime in row 1, column 1. The numbers must read in descending order from top to bottom and then left to right. The output table must have exactly 8 columns unless there are fewer than 9 values to display, in which case only a single row is necessary. The numbers must each fit into a field of size 10, right justified. For example, this displays the first 20 numbers in the correct format. Note that these are NOT prime numbers but simply the location in the output table each prime would take: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Sieve algorithm A list is a collection of similar elements in which each element has a specified position (e.g. sequence number) in the list. A list can be implemented in C as a 1-D array. Steps in determining the primes: 1. Write a list of numbers from 2 to the largest number you want to test for primacy. Call this List A. 2. Write the number 2, the first prime number, into another list for primes found. Call this List B. 3. Strike off 2 and all multiples of 2 from List A. 4. The first remaining number in List A is a prime number. Write this number into List B. 5. Strike off this number and all multiples of this number from List A. Page 2 of 3
Assignment 3: Fun with Primes
EE312 The University of Texas at Austin Spring 2008 6. Repeat steps 4 through 6 until no more numbers are left in List A. Actually, for efficiency, the crossing-off of multiples can be finished at the midpoint of the range or at the square root of the largest number. 7. List B now contains all the prime numbers in that range. List A can be discarded. Processing of Primes for Additional Characteristics After the list of primes are found and output, the list of primes should be processed again to find and report those that have the following additional characteristics. Find and report the list of primes for which two consecutive prime numbers have a difference of four. For example 11 7 = 4 In other words find Pn+1,Pn such that Pn+1 Pn= 4 Output the list of the pairs of numbers whose difference is 4, with each pair on a separate line. The above example would output something like: The pair of primes 7,11 has a difference of 4 Next, find all those primes in the list (B) which are CPSPs of order-3. A Consecutive-Prime Sum Prime (CPSP) of order-3 is a prime number that is the sum of three consecutive prime numbers. For example, when added together, 5, 7, and 11 (all primes in sequence) equal 23 (another prime number). In other words, find those values of Pn, Pn+1, Pn+2, Pk such that: Pn + Pn+1+ Pn+2 = Pk (Pk does not have to be the next prime in sequence) Output the four primes in the format Pn+ Pn+1 + Pn+2 = Pk, with each group of four on a separate line. For example, the above would output something like: 5 + 7 + 11 = 23 (which is a CPSP of order-3) Design requirements You must implement the solution using arrays. You may use as many functions as you find necessary to improve modularity and understandability of your program. You must include a minimum of two functions besides the main function. These should be written with a view of reusing them in a future ee312 course assignment.
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