2016-01-24 (Sunday)

Today, I learned that:

The largest prime number ever found was announced last Wednesday, January 20, 2016. So, what is a prime number and what is it good for?

A prime number is defined as a natural number (a positive integer) greather than 1, which cannot be evenly divided by any other natural number than 1 and itself. Examples of such numbers are 2, 3, 5, 7, 11, etc. It has been proven that there are an infinite quantity of prime numbers.

Prime numbers have been known for a long time, e.g. Euclid’s Elements (300 years BC) already mentions them, and in the beginning of the 17th century, a French monk named Marin Mersenne devised a formula, of the form 2p – 1, where p=1 is a prime number, to be used to check for unknown prime numbers. In fact, the largest prime number, which is exactly 274.207.281 − 1, consists of more than 22 million digits, and the search for bigger numbers continue. Please see the three references below for more information about prime numbers in general and also about the discovery of the currently biggest prime number, including an interview with Curtis Cooper, the leader of the project that discovered it.

One of the practical usages of prime numbers is in public-key cryptography, where two large prime numbers are multiplied to obtain a product that it is extremely difficult to factorize and thus break the code. But the search for these very big numbers does not seem to have any major practical use today, although they are very well fitted to test the speed performance of computer hardware.

And speaking about cryptography, having means of obtaining secure data streams is of course essential when we want to communicate data from one point to another. The current standard for data communication in the world is based upon what is called fourth-generation (4G) technology, and although it offers very fast rates of data communication, there are applications that demand even faster data transmission speeds. Examples of such applications are some components of the ‘Internet of Things’ (e.g. driver-less cars), and also in remote surgery, when the patient is in a hospital somewhere in the world, and at the same time the head surgeon is in a totally different place, performing the surgery via advanced, fast video and manipulation technologies.

For that and other purposes, last Friday, January 22, 2016, TeliaSonera and Ericsson announced that in 2018, they will start 5G networks in Stockholm and Tallinn. The rest of Sweden should see 5G in use in 2020.

Update on 2016-01-27: Today’s program of ‘Vetenskapens värld’ on Radio Sweden’s domestic channel P1 penetrates into the 5G technology. It will be a standard mostly used for machine to machine communication, and there are good hopes that one standard will be used everywhere on Earth, with speeds 100 times higher than the current 4G standard. See reference 7 below.

… That’s what I learned in school!

Refs.:

1: https://en.wikipedia.org/wiki/Prime_number

2: http://www.mersenne.org/primes/?press=M74207281

3: https://www.youtube.com/watch?v=q5ozBnrd5Zc

4: https://en.wikipedia.org/wiki/Public-key_cryptography

5: http://news.err.ee/v/scitech/fd66b9ee-1a44-4d13-aa6c-1f687812b2b8/

6: https://en.wikipedia.org/wiki/List_of_mobile_phone_generations

7: http://sverigesradio.se/sida/avsnitt/668029?programid=412

+: https://www.youtube.com/watch?v=VucczIg98Gw

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