Download Assignment 5 Practice with Functions

Assignment 5
Practice with Functions
Write a program that computes prime numbers. A prime number, recall, is an integer >= 2 that
is divisible only by itself and 1. This program will:
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Compute either the nth prime or primes in a range
Not permit the user to proceed without having entered valid input
Be modularized, that is, decomposed into several functions
Execution:
1. The program will ask the user to input ‘r’ or ‘n’, where ‘r’ indicates a range of prime
numbers, and ‘n indicates the nth prime number. The first five prime numbers are
2,3,5,7,11. 11 is the 5th prime number.
2. If the user enters anything except ‘r’ or ‘n’, the program displays “Invalid Entry” and
returns to step 1. You can assume that your user will enter only alphabetic characters.
3. Steps 1 and 2, will require the following Boolean function:
#returns True if inp is ‘r’ or ‘n’, returns False otherwise
def check_inp(inp):
4. If the user enters ‘n’, the program computes and displays the nth prime number and
exits. This step requires the following function:
#displays the nth prime number
def gen_nth(n):
gen_nth requires the Boolean function is_prime, documented in step 7
5. If the user enters ‘r’, the program requests two integers in the range [low … high]. low is
>= 2 and low < high. You can assume that your user will enter integers. This step
requires the following Boolean function:
#returns True if parameters meet the range criteria, False otherwise
def check_range(low, high)
If check_range(low, high) returns False, the program displays an error message and
requests the integers again.
6. If the range meets the stated criteria, the program will invoke this function and exit:
#displays all prime numbers in the range [low .. high]
def gen_range(low, high)
gen_range requires the Boolean function is_prime, documented in step 7.
7. Both gen_nth and gen_range that generate require the following Boolean function:
#returns True if n is prime, False otherwise
def is_prime(n):
To do this problem, proceed incrementally:
A.
B.
C.
D.
E.
Code and test steps 1, 2, 3
Code and test step 5
Code and test step 7
Code and test step 4
Code and test step 6
Bonus:
Once all steps have been thoroughly tested, see if you can refine is_prime(n). There is
an obvious way to check for primality and a less obvious, but much more efficient way.
Hint: an integer that is not prime is composite. A composite integer has (at least) two
factors. Decompose a few small integers into two factors. Do you see a pattern in the
sizes of the factors with respect to the composite integer?