Quiz Date: Wed, Mar 12, 2003
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Good
luck!
Question 1: Goldbach's Conjecture states that every even number larger than 2 is the sum of two prime numbers. Interestingly, nobody has ever proven it to be true, but it sure seems to be true. Consider the following examples:
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7
12 = 5 + 7
14 = 3 + 11
16 = 3 + 13
...
Write a Java program which empirically confirms Goldbach's Conjecture by repeatedly reading in an even integer n (halting when n < 4) and printing out that number as the sum of two primes (of course, your program must find the primes which sum to n). If n is odd, just print out that it is odd.
Here is exactly how your program should work:
Enter an even integer [<4 to exit]: 10
10 = 5 + 5
Enter an even integer [<4 to exit]: 17
17 is odd. Please try again.
Enter an even integer [<4 to exit]: 16
16 = 3 + 13
Enter an even integer [<4 to exit]: 0
Goodbye!
Hint:
for each number p which is less than n, check if p is prime, then check
if (n-p) is also prime. If both are
true, then p and (n-p) are the two primes which sum to n, because p + (n-p) ==
n.
Hint: Even if you cannot solve this problem outright, write as much of the solution as you can!
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