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.
- 6 = 3 + 3
- 12 = 7 + 5
- 20 = 7 + 13
Play with an interactive version of this conjecture here.
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 × 1018 or 4,000,000,000,000,000,000.
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.