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The Wonder Number Lessons

Lesson No. 16:  Goldbach's Conjecture

The Wonder Number Board can be used to examine interesting mathematical theories.  One theory particularly suited for examination is Goldbach’s Conjecture. Prussian mathematician Christian Goldbach was the son of a pastor.  He traveled throughout Europe and came into contact with many great mathematical thinkers of his era and was at one time a tutor for Peter the Great. 

Goldbach postulated that every even integer greater than 2 can be written as the sum of two prime numbers. 

This is a good lesson to reinforce the concept of prime numbers and is a fun exercise for curious students who like discovering more about math.  Give them an even number greater than 2 and then let them look for two prime numbers that add up to that number.  Also tell the student that sometimes there are more than two pairs of primes which can add up to the number.

The first number we will use to test Goldbach’s Conjecture is 8. The two prime numbers that add up to 8 are 3 and 5 (see fig 81).

Another example is 32.  There are two sets of prime numbers that add up to 32.  The first pair is 29 and 3.  The second pair is 19 and 13 (see fig 82).

The next example is 68.  There are two sets of prime numbers that add up to 68.  The first pair is 61 and 7.  The second pair is 37 and 31 (see fig 83).