### Goldbach's Conjecture (Due 24 Mar 2017)

In 1742, a German amateur mathematician named Christian Goldbach wrote
to Leonhard Euler with the following conjecture:

* Every number greater than 2 can be written as the sum of three
prime numbers. *

In his conjecture, Goldbach was considering 1 as a prime number. By
convention we no longer consider 1 as a prime number. And Euler later
modified the conjecture as follows:

* Every even number greater than or equal to 4 can be expressed as
the sum of two prime numbers. *

For example:

- 8 = 3 + 5
- 20 = 3 + 17 = 7 + 13
- 42 = 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23

There is no formal proof of this conjecture. However, we can verify
Goldbach's conjecture in certain ranges. For this programming assignment
you are asked to verify Goldbach's conjecture in a user defined range.
You will prompt the user to enter the range and then your program will
print out all the even numbers in that range (inclusive of the end
points) in the form *n = a + b*, where *a* and *b* are
prime numbers and a <= b. Each even number should be on a separate
line followed by *all* possible unique pairs of prime numbers.
Your sample output should look like this:

Enter the lower limit: 4
Enter the upper limit: 100
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
....
....
100 = ....

You will do the following error checking on the input:

- Lower limit is equal to or greater than 4
- Both lower limit and upper limit are even
- Lower limit is strictly less than upper limit

Even if only one of these conditions fails, prompt the user
to enter both the limits repeatedly.
Your program should have a good, clean logical structure. You **must**
make use of the function *is_prime()* that we developed in class. We will
be looking at good documentation, descriptive variable names, and adherence
to the coding convention mentioned below. Your file *Goldbach.py* will
have the following header:

# File: Goldbach.py
# Description:
# Student Name:
# Student UT EID:
# Course Name: CS 303E
# Unique Number:
# Date Created:
# Date Last Modified:

Use the Canvas
program to submit your **Goldbach.py** file.
We should receive your work by 11 PM on Friday, 24 Mar 2017.
There will be substantial penalties if you do not adhere to the
guidelines.

- Your Python program should have the header with the proper
documentation.
- Your code must run before submission on the command line.
- You should be submitting your file through the web based
*Canvas* program. We will not accept files e-mailed to us.
- Here is the Grading Criteria.