Our look at math conjectures continues with Goldbach’s Conjecture.

Remember that a conjecture is a statement believed to be true, but unproven. It’s an authentic, unsolved problem, but simple enough for students to explore.

Goldbach’s Conjecture states:

Every even integer greater than two can be written as the sum of two primes.

### Examples

- 6 = 3 + 3
- 12 = 7 + 5
- 20 = 7 + 13

Play with an interactive version of this conjecture here.

### Unproven

As with all conjectures, mathematicians believe this to be true for all cases, but no one has proven it yet. The best part is: they’ve had *over 270 years* – Christian Goldbach made this conjecture in 1742!

The Goldbach Conjecture has, however, been verified to work for numbers up to 4 × 10^{18} or 4,000,000,000,000,000,000.

### Three Primes

Christian Goldbach also made a related conjecture: every integer (odd *or* even) greater than five is the sum of three primes.

- 6 = 2 + 2 + 2
- 11 = 5 + 3 + 3
- 17 = 5 + 5 + 7

Again, this is strongly believed to be true, but has not been proven yet for all numbers.

Have your students explore these conjectures, looking for evidence that it’s true, or a *counter-example* that disproves the conjecture.

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