./goldbach
Goldbach's Conjecture asserts that every even integer greater than 2 is equal to the sum of two primes.
Input threshold integer to check for an exception: 100000001
Checking up to 100000000...
There are [49999999] even numbers in the range (4 - 100000000).
[49999999] fulfilled Goldbach's Conjecture in this check.
Let's say that the user inputs '33'. The program will check Goldbach's Conjecture up to 32, assigned to the variable 'userInput'. The program will increment a variable called countUp in twos (countUp begins at 4), until it is equal to userInput.
| Place in file | What's happening |
|---|---|
| OUTER LOOP | (a = 0), and (b = countUp) for a given value of countUp in OUTER LOOP. |
| INNER LOOP | These variables change as a locked pair: (a++) and (b--). |
| As such, (a + b) will always be equal to the OUTER LOOP value of countUp. | |
| If on a given loop (both a and b are primes), program breaks to the OUTER LOOP. | |
| Otherwise, it keeps going until (a == b) and then breaks. | |
| OUTER LOOP | The program checks whether the INNER LOOP found (a && b are primes). |
| When it does, countup increments by 2. Otherwise, the program ends. |
Let's say we're on the 13th loop of the OUTER loop, where (userInput == 32), and (countUp == 28).
Countup started at 4, and counted up in twos 13 times.
The program proceeds as such:
__13th ITERATION_ OUTER WHILE LOOP INNER WHILE LOOP
userInput = 32
countUp = 28
a = 0
b = 28
a++ | b--
1 (NP) | 27 (NP)
2 (P) | 26 (NP)
3 (P) | 25 (NP)
4 (NP) | 24 (NP)
5 (P) | 23 (P) <-- BOTH PRIMES
-- BREAK;
-- countup += 2;
__14th ITERATION_ userInput = 32
countUp = 30
a = 0
b = 30
a++ | b--
1 (NP) | 29 (P)
2 (P) | 28 (NP)
...
... and so on