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Finding patterns in prime numbers

The mystery surrounding prime numbers and experiments with visualization

May 14, 2013

Prime numbers are extremely important because they are the basis for many daily applications.

In fact, thanks to the primes, we can today count on cryptosystems, that allow us to have home banking service, email or online shopping (among other things).

Prime numbers have been studied for thousands of years and still remain one of the “mysteries” of mathematics …

Although Euclid contributed to study of prime numbers – he came to the conclusion that they are infinite in number – and Fermat and Mersenne discovered that numbers that can be written under a certain form are primes​​, there are still a multitude of these numbers that is not known and on which research is still being done.

In fact, in the last January, a new prime number was discovered, 257,885,161-1, bringing a new enthusiasm to mathematicians because of the potential importance of the discovery.

The mystery surrounding prime numbers is that we do not know a single pattern to describe them all, a property that makes them so precious and useful!

Despite this, it is possible to visualize the existence of patterns in primes if we restrict ourselves to the analysis of some of these numbers.

Let’s look at some examples:

Odd prime numbers < 8192
Odd prime numbers < 8192 (Source)

 

100 million primes ​​- 2D visualization
100 million primes ​​- 2D visualization (Source)

 

Model of periodic curves superimposed to describe patterns of prime numbers (Source)
Model of periodic curves superimposed to describe patterns of prime numbers (Source)

 

Primes from 1 to 62500
Primes from 1 to 62500 (Source)

 

Interesting, isn’t it? You can also find other ways of visualizing some prime numbers,but I could not help to highlight the famous sieve of Eratosthenes, an important contribution of early study of prime numbers.

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Sieve of Eratosthenes (Source)

 

Written by Susana Pereira

Susana Simões Pereira, maths teacher and PhD in science teaching and communication. I enjoy games and photography and I'm passionate for science and art, specially when together in the same context. You can follow my updates on Twitter, LinkedIn and Facebook.

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