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## Mersenne and his primes

On Thursday my further maths AS class and I arrived at the classroom to discover an interesting slide still displayed on the board from a previous lesson.

My colleague had been teaching a lesson on prime numbers to his year 9 class and the slide in question was about finding new primes, how much money you can earn if you do, why this is and the “Great Internet Mersenne Primes Search” (and its unfortunate acronym).

A discussion ensued about cryptography and the uses of primes. It then moved onto the mathematical monk himself and his work in number theory. In particular that he noticed that numbers of the form (2^p)-1,  where p is a prime, are usually prime. These Mersenne primes have fascinated me for years. How comes so many of them are primes? Why aren’t the all?!

The class were equally fascinated and we had a great discussion. We also managed to link it to a discussion we had had the previous lesson about p vs np, as trying to factorise (2^11)-1 is fairly difficult,  but it is really easy to check if 23 is a factor. The class wondered if they could set a computer to test massive numbers for prime factors. I explained that yes, you could, but it would take so long to check the massive numbers it would be worthless. So if they can find a way to do it quickly they could become very rich.

We lost around twenty minutes of matrices time, but we have plenty of time to make it up. I think all pupils left with a deeper and broader mathematical knowledge and a healthy thirst to know more- which is at least as important.

Categories: #MTBoS, A Level, Maths, Teaching
1. January 18, 2014 at 11:00 am

Reblogged this on The Echo Chamber.