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# Prime Numbers

Prime numbers are a special category of natural numbers (or positive integers) which are exactly divisible by 1 and by itself. So, a prime number has exactly two divisors. Prime number is a number which is greater than 1 and which can be efficiently divided by 1 and by itself, not by any other number. It is also a whole number.

An Integer P > 1 is called a prime number when its only divisors are 1 and P. Any number m > 1 which is not a prime is called a composite.

Theorem: Every composite number could be factored into prime factors and each of these is unique in nature.Simple properties of primes:

(a) A prime 'p' is either relatively prime to a number 'n' or divide it.
(b) A product is divisible by a prime 'p' only when 'p' divides one of the factors.
(c) Every n > 1 is divisible by some prime.

 Related Calculators Calculate Prime Number Calculate Prime Factors Find Prime Factorization Calculator Prime Factorization Tree Calculator

## What is a Prime Number?

Prime numbers are a special category of natural numbers or positive integers which are exactly divisible by 1 and the number itself. So, a prime number has exactly two divisors.
Largest Prime Number
The largest known prime number is 2$^{74,207,281}$ - 1 as of January 2016. It is said to have 22,338,618 digits.

Smallest Prime Number
As we know, 2 is the smallest prime number.

### Are all Prime Numbers Odd?

Yes, all prime numbers are odd, but only even prime number is 2. Since every other even number can be divide by a 2.

## List of Prime Numbers

Till now, we have explained the concept of prime numbers and given below is list of prime numbers for your better knowledge.
The list from 1 to 200 are as follows:

 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47  53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199

## Is 1 a Prime Number?

According to the prime number definition, we can say that 1 is not a prime number. The definition says that a prime number should have exactly two divisors. But 1 has only one divisor. So, 1 is not a prime number.

### Is 2 a Prime Number?

Yes, 2 is a prime number because it is divisible by itself and 1.

## Prime Number Theorem

$\lim_{x \to \infty }$ $\frac{P(x)}{\frac{(x)}{(log x)}}$ =1.