ATOMS OF MATHEMATICS

Consider this,

6= 2 * 3
9 = 3* 3
12 = 2* 2* 3

The kind of numbers like 6, 9, 12 are called composite numbers because they can be broken down into smaller numbers.
But numbers like 2, 3, 7, 11 cannot be split up into whole numbers. They are divisible by 1 and by themselves only. These numbers are called prime numbers. They behave like "atoms" in the number system. We can build other composite numbers using them in an unique way. For example, 28 can be expressed as 7 * 2* 2. This is the only way to write 28 using primes.
Another example:6545448 = 2^3*3^5*7*13*37

The list of prime numbers below 100 is given below.
2, 3, 5, 7, 11, 13, 17, 19, 23 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
There are 25 primes between 1 and 100. But only 14 primes between 900 and 1000. There is no formula to find the prime numbers. There is no pattern in the appearance of primes. Yet, the umber of prime numbers are limitless. The largest known prime is 2^24036583-1.

There is rough formula to calculate the number of primes up to N.
Number of primes = N/log N (log of base e)
This formula is also called prime number theorem.

There is one prime use for prime numbers.
Multiply to 2 large primes and release the product. It is very difficult to extricate the 2 primes from the product and the process will consume lot of computer time.(try to get back 2 primes from 8633- a toy problem)
This principle is used in public key cryptography(sending secrets in open channels). Example: Credit card transaction.

Final note: I said the prime number 5 is unbreakable. Please allow me to correct myself now. 5 can be split up into integer complex numbers as follows.

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