Prime Numbers

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. 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 compositely 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 divided 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.

What are Prime Numbers? Prime numbers are natural numbers which have only two divisors which are 1 and the number itself.

These numbers comes under the study of elementary math. Learn to distinguish all the prime numbers from the composite numbers.

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.

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

m₃₉ = 2^13,466,917-1 is the largest prime number.

Smallest Prime Number

As we know, 2 is the smallest prime number.

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

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.

Let's identify whether the following numbers are prime or not

Let P(x) be the number of prime numbers less than x, where x > 1 and x is a real number. Then the prime number theorem states

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

This asymptotic formula precisely gives the value to which prime number density approaches as the numbers grow larger and larger. It has been termed as one of the most beautiful and important theorems in the history of mathematics and number theory.