CS 670, Homework 2.
Due: Tuesday, January 22 at 11:59pm.
Points: 20 HW points.

For questions (1), (2), (4) - put those answers in your .txt file.
For qeustions (3) - create those programs and leave them in 
~yourusername/cs670/handin/

(1)
Name: 

(2) List anyone that you talked to or worked with on your HW.  Remember
    to review the policy in the syllabus on collaborating on HW's.
Collaborators:

(3) Modify your perfectCount program as follows.
    (a) If you had mistakes with not locking updates to shared variables, 
        fix those mistakes.
    (b) Rename the program perfectCount.cpp, and convert all the 
        long long int's to be mpz_class GMP variables.  See 
	factorOpenMP4.cpp for how to do this.
	Now the program should work for arbitrarily large numbers.
    (c) Rather than testing all numbers, only test numbers that are of the 
        form 2^(p-1)*(2^p - 1).  These numbers are prime precisely when 
	2^p - 1 is prime, and there are conjectures stating that all perfect 
	numbers are of this form.  So, rather than testing 2, 3, 4, ...
	if each is prime, instead do the following.  For p=2, 3, 4, ...,
	test if 2^p - 1 is prime.  If it is, then conclude that 
	2^(p-1) * (2^p - 1) is perfect.

	For more on this formula for perfect numbers, check the wikipedia
	article on perfect numbers.

	Still make your program so that it tests numbers up to the command 
	line argument that is given, but you will only test numbers of the 
	special form just mentioned.  So it will still be the case that
	./perfectCount 30
	will say 2, and 
	./perfectCount 10000
	will say 4.  But we should be able to go to much higher numbers.

	The program should continue to use multiple threads using OpenMP.

(4) For your program from (), what is the largest value of n
    (a) where your program finishes in 1 second,
    (b) where your program finishes in 10 seconds,
    (c) where your program finishes in 1 minute?

    And what are the counts returned for those values of n?