How are prime numbers used?

Prime numbers are also useful in generating random numbers. They helps us in avoid pattern and arrive at actual random series. Prime numbers are also used in designing gears. Just imagine if number of teeth in a gear is prime number, it will give it certain uniqueness. They are also used in architecture and acoustic design.

In fact what is generally typical about mathematics is that one can generate ideas around its concepts and use it wherever one feels using it. Mathematics is more of a tool and while it is extensively used in physical sciences, it is also used a lot in social sciences (particularly statistics).

The most notable use of prime numbers in present day world is, however, in encryption technology or cryptography. In fact you are using it every time you access a website whose URL starts with **https://** - like accessing your bank accounts or even Socratic. The only thing is that stronger the desired security, stronger the encryption and larger the size of prime numbers used in encryption.

In fact RSA algorithm (used extensively on secured sites) uses a number #n# which is a product of two very large prime numbers #p# and #q# and relies on the difficulty of identifying factors of #n# for some body who may not have information on #p# and #q#.

Try factorizing a very large #n#, which is a product of two primes such as #2202510496045793#. This may still be easier using computers. But the kind of large prime numbers that are used in encryption are much larger and by the time even computers break it, the transaction may be complete.

Incidentally, #2202510496045793=32452867xx67867979#.

At school level, a solid understanding of prime numbers and factors has many uses, because all numbers are made up of prime numbers.

If a number is expressed as the product of its prime factors, then

Firstly:
all the properties of that number can be seen at a glance.
ie is it, odd, even?,
prime, composite?, a square, a cube or any other power?

Secondly:
all the factors of a number can be determined by using different combinations of the prime factors.

Thirdly:
Once the product of the prime factors is known, it is easy to calculate the square root, cube root or any other root.

Fourthly
It is possible to ascertain how the number can be made into a square or cube etc by multiplying by missing factors.

Fifthly
Using prime factors is an easy way of finding HCF and LCM of larger numbers.

Also in factoring quadratic trinomials,

The use of prime numbers is sadly under-utilised in the junior secondary phase, where students are asked to write a number as the product of its prime factors, but little use is made of it.