Adam Spencer: why I fell in love with monster prime numbers

Adam Spencer, an Australian mathematician speaks about his passion regarding prime numbers on the TED website. His speech starts with a funny story from his life concerning his first adventures with mathematics. When he was at school, he answered an ironic affirmation made by his teacher comparing something that can’t work with the act of “trying to put a square peg through a round hole”. He disappointed him by simply explaining that “if the diagonal of the square is less than the diameter of the circle, well, the square peg will pass quite easily through the round hole”. He fell in love with maths at a very young age because, as he says, maths is present everywhere in the universe.

The true topic of the speech is what we call prime numbers, but there is nothing complicated in what he says. Just remember that a prime number is a number that can’t be decomposed into factors. For example, 7 is prime because it is just 1*7, while 6 is not prime because it is 3*2 as well as 1*6.

Prime numbers are endless: there is no biggest prime number. This was proved by the excellent mathematician Euclid thousands of years ago, when the only means people could use to prove an argument was their own mind: no computers, no calculators.

That said, what is the biggest prime number we know so far? Generally the number, two to the power of a prime number, minus one, is itself a prime number. Therefore, (2^5)-1 is prime. This is not always true, but it’s quite easy to verify if a number of that form is prime or not.

During the centuries, the biggest prime number ever known has kept growing. Now, with the help of computers, it is increasing year by year.

The biggest prime number discovered by Euler is (2 ^ 31) – 1. In 1961, the biggest prime number known was (2^4423)-1, in 1985 (2^216091)-1, in 1996 (2^1398269)-1.

These days, the highest prime number that we know of is 2^57885161-1. It is a very recent discovery due to Dr. Curtis Cooper. To help you understand how big this number is, just know that if we typed it in a text file, it would be 22 megabytes, while if we wrote it out as a book, it would be longer than all the Harry Potter novels put together.

Practically, why should all this be important? There are some reasons why we should be interested in it. First, since proving that a number is prime requires a series of repetitive operations done by machine, large prime numbers are a very good way of testing the speed and the accuracy of computer chips.

Furthermore, looking for prime numbers is similar to the work people are doing in unraveling RNA sequences, in searching through data from SETI and other astronomical projects.

In conclusion, what Spencer finds so beautiful about this kind of number is that, before confirming the existence of a new one, we suppose it exists, then we set about finding it. This represents for him the essence of being human.

#Primenumbers #Maths