An challenging and fun activity for students is be to ask them if they can write every even number up to 100 (or beyond) as the sum of two primes. For example, 6 = 3+3, 8=5+3, 10=5+5….30=17+13….90= 83+7, etc. This is good practice for memorizing the prime numbers through activity rather than by rote. It is also good mental math. Students may also take the approach of rather than trying to find each number one at a time, just adding up combinations of primes and see what they get! For example, if they want to get 48 and they try 23+23 and see it doesn’t work, don’t discard it! They just found 46!
Goldbach’s conjecture surmises that every even number greater than 4 can be written as the sum of two odd primes. It has still not been proven. Perhaps one of our students will prove (or disprove) this famous conjecture.
Two funny things about the name. First, I like to ask who came up with Goldbach’s conjecture and then say that Mr. Conjecture did (he seemed to do a lot of math!) Second, it reminds me of Goldbug from the Richard Scarry books. He always drove the tiny car and was really hard to find in the illustrations!