Prime and Powers Investigation
'Each of us has a unique DNA structure in every cell of our body. Prime Numbers are the DNA of the number system. Discover why, and solve the murder mystery . . . '
Why are "Prime" numbers "prime" i.e. what's so special about them? Why are they called the "DNA of the number system"? Using calculators, divisibility tests knowledge and perhaps some "Prime Factor Decomposition" techniques, this activity aims to find which numbers from 1 to 100 can and can't be made by multiplying together prime numbers.
- List as many Prime Numbers as possible in 2 minutes [1 is not prime because it has only one factor (not two)]
- Investigate which of the numbers from 1 to 100 can be made from multiplying two or more prime numbers (or the same one again and again!) together from the above brainstorm of prime numbers. There are many strategies to be found based on multiples, factors and divisibility tests, that can save lots of time when compared to trying at random to find the prime number multiplication of any given number.
- Brainstorm what "divisibility" tests there might be for different multiples / timestables.
- Explore the concept of "undeniable reasoning" and "proof" through the formulation of an argument based on multiples etc. that means this entire problem can be solved in about 30seconds to 1minute!
- From the investigation results, why might prime numbers be considered "the DNA of the number system".
- Use prime factor decompositions to find the squares, cubes, fourth, fifth roots of the number clues left by the murderer. Alternatively, the above calculator help sheet can be used to find the root of each number clue.