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Perfect Numbers and Mersenne Primes

Number Powerpoint Presentation

Perfect Numbers and Mersenne Primes

This is another major presentation for the enrichment area and is aimed primarily at the gifted and talented student but the early parts are accessible to all. As one Head of Maths commented recently whilst showing it to her department “It reminded everybody of why they wanted to become maths teachers”. We start off by looking at abundant and deficient numbers and then turn to perfect numbers. The students are given a worksheet in which they have to classify all numbers to fifty in this way. Their challenge is to find the second perfect number and investigate some given statements. Perfect numbers in Greek mathematics are then looked at followed by a history of their discovery and rarity. We then look at the strong connection between Mersenne primes and perfect numbers. We discuss GIMPS and go on to show how to find the next perfect number each time that a new Mersenne prime is identified. The students are first given the opportunity to find this relationship themselves. We conclude with a NEWS FLASH about the 44th Mersenne prime (and therefore 44th perfect number) having been found on 4th September 2006. Enjoy!

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