Mathematics is a science of patterns. Among the different patterns depicted by mathematics, there has been a fundamental and intriguing pattern of prime numbers, which has been a subject of interest of many mathematicians since ancient times. Mathematics has acquired the status of a language in itself with its own set of rules and symbols, explaining many naturally-occurring happenings in the world.

Among the integers, there are many subsets, like, even numbers and odd numbers, which are mutually exclusive sets of numbers and also there is a set of numbers which is of the prime numbers.

Prime numbers are unique in a way that number 1 and the prime number itself are the only factors of the number. Or in other words, there is no number other than 1 and the prime number itself, which can divide the prime number with the remainder as zero. For example, number 3, 5, 7, 11, 13, 17, 19, 23 etc., are all prime numbers.

How many prime numbers are there is an elusive question, and Euclid proved that there are infinitesimally many.

Another distinguishing feature of the prime numbers is that we don’t know yet what pattern prime numbers follow. While the definition of prime numbers is simple and straightforward, many mathematicians, even after working on the puzzle for a long time, cannot find the way or the pattern using which the prime numbers sprout up.

Thus, finding the algorithm that can tell the next prime number is still an ongoing challenge that keeps the topic of prime numbers very juicy. While mathematics is the study of pattern, the pattern of prime numbers remains unknown.

This special property of prime numbers makes it useful for a number of applications; let us have a look into them briefly below :

- In recent times, online shopping is the default way to go and, in some ways, already ahead of brick and mortar shops. When making an online payment for the shopping, which is done using a credit card, the credit card number is sent over the network. Since it is sensitive information, the credit card number is encrypted. The most common encryption used is RSA, and it employs the prime numbers to make sure that the encryption cannot be decrypted by anyone except one who has the key to decrypt it. This encryption technique is based on the fact that it takes a lot of time to find the prime factors of a very large number. So, if we take two very large prime numbers and multiply them, then for the computer, it will be very difficult to know which two prime numbers form the number.
- If you are dealing with mathematics, chances are you are dealing with prime numbers as it has often been said that the prime numbers are the atoms of mathematics or the building blocks of mathematics. It is so because any number, when broken down into its factors in the end, can be defined as the multiplication of prime numbers.
- In music, all the structure of tonal music like chords, scales, harmony, modality, it is possible to represent them all mathematically as rational prime number structures.
- In nature, many interesting examples of prime numbers exist as certain insects like cicadas come out of the underground habitat only after the prime number of years, like 17 years.
- Often flowers have an odd number of petals, and more often than not, they are prime numbers. For example, five is a commonly found number of petals in flowers.