Prime numbers are cool, and this can be proved by only staying in touch with the basic facts about them. Carl Sagan pointed out in his novel that there is particular importance of prime numbers status like the most fundamental building blocks of all numbers. These building blocks themselves are the blocks which help in the understanding of the universe. The aliens choose to send a long string of prime numbers as proof that their message is intelligent and not natural. Prime numbers are one thing which cannot be changed due to the difference in psychology, lifestyle, or evolutionary history. Irrespective of what an advanced alien-life form looks or thinks, if it has the sense to understand the world around it, it will have the concept of prime.
Most people are familiar with the basic idea of prime numbers. However, if you need a reminder, read the rest of this. Primes are the set of all numbers which can only be divided by 1 and themselves. No other division with any different number is possible. Numbers like 2,3,5,7, and 11 are all prime numbers. When you are looking for primes, you can remove half of the numbers from the list along with the multiples of three, four, five, etc. After a particular time, no numbers are left even though there is an infinite number of primes, but they are less frequent in use. This is one of the reasons the prime numbers are so impressive. The number line with prime numbers goes up to infinity, but the whole number line can also be produced using only the prime numbers. For example, 12 can be rewritten as 2*2*3, and both 2 and 3 are primes. Similarly, 155 can also be written as 5*31.
There is also a mathematical proof which assures that a combination of prime numbers can be multiplied to produce any number at all. Primes are the entire set of numbers which are left over when we rewrite all numbers as their lowest possible combination of integers. When no more factoring is likely all the numbers which are left over are prime. This is the reason; primes are so relevant in some fields. They have unique properties for factorization. One of these properties is that when it is relatively easy to find a larger prime number, it is tough to factor large numbers back into primes. One thing is that 20 is 2*2*5 and another is to figure out that 2,244,354 is (2*3*7*53437). You can imagine how hard it can be to factor a number with 50 or 100 digits. It is so hard that despite mathematicians working at the problem for hundreds of years there is still no method which can factor huge numbers efficiently.
This might sound like a problem. However, it is an opportunity for the uses prime numbers. Latest encryption algorithms exploit the fact that we can take two large primes and multiply them to get a new, super-large number. However, no computer created so far can take that super-large number and quickly find which two prime numbers are making it. Modern super-computer can take to solve a 256-bit factorization problem for a longer time than the current age of the universe, and will still not get the right answer. Computer encryption is continuously used in our routine lives which means that we are making use of prime numbers regularly as well. We rely on their unique numerical properties for the protection of the cyber-age way of life. It is not meaningless research to understand the prime numbers, as all of the security these days rely on the limitations of that understanding.
There are also chances that new strategies or hardware like quantum computers may lead to quicker prime factorization of large numbers which can break modern encryption. If this happens, anything that computers can do without undoing it easily, will be of interest to the computer security. There can be various important uses of prime numbers. Cicadas time their life cycles by prime numbers, modern screens use these to define color intensities of pixels, manufacturers use to get rid of harmonics in their products. However, these uses are nothing as compared to the fact that these numbers form the basis of our modern computer security. Prime numbers are used by us in everyday routine and are a vital part of our society.