Prime Numbers

A prime Number is that positive integer which has exactly two unique factors, 1 and itself. So, a prime number is only divisible by 1 and itself.

In other word, any whole number greater than 1 that is divisible only by 1 and itself, is defined as a prime number.

Notes:

• 2 is the only even prime number and the smallest prime number
• Negative numbers are not prime numbers
• 0 & 1 these two are not prime number

Finding the Prime Number 

Shortcut for 1-100 Count Reverse 100-1				ABC BBC BBDD 123 223 2244
1-10 = 4	11-20 = 4	21-30 = 2	31-40 = 2		41-50 = 3	1-100 Total Prime Numbers 25
2,3,5,7	11,13,17,19	23, 29	31,37		41,43,47
51-60 = 2	61-70 = 2	71-80 = 3	81-90 = 2		91-100 = 1
53,59	61,67	71,73,79	83,89		97

Shortcut (more than 100)

 

1^st, Approximate square root of the number

2^nd , Find the prime numbers less than the approximate square root of the number

3^rd, Check is it/the number divisible by the prime numbers or not

Finally, If the number cannot be divisible by the prime numbers than the number is prime

 

Example: Find 161 is prime or not

 

Approximate square root of 161 is 13

Prime less than 13 is 2,3,5,7

161 is divisible by 7

So, 161 is not a prime number

Formula 1: 2 is the only even prime number. And only two consecutive natural numbers which are prime are 2 and 3. Apart from those, every prime number can be written in the form of 6n + 1 or 6n – 1 (except the multiples of prime numbers, i.e. 2, 3, 5, 7, 11), where n is a natural number.

For example:

6(1) – 1 = 5
6(1) + 1 = 7
6(2) – 1 = 11
6(2) + 1 = 13
6(3) – 1 = 17
6(3) + 1 = 19
6(4) – 1 = 23
6(4) + 1 = 25 (multiple of 5)

 

Formula 2: To know the prime numbers greater than 40, the below formula can be used.
n2 + n + 41, where n = 0, 1, 2, ….., 39

For example:

(0)2 + 0 + 0 = 41
(1)2 + 1 + 41 = 43
(2)2 + 2 + 41 = 47

Twin Prime numbers

The prime numbers with only one composite number between them are called twin prime numbers or twin primes. The other definition of twin prime numbers is the pair of prime numbers that differ by 2 only. For example, 3 and 5 are twin primes because 5 – 3 = 2.

The other examples of twin prime numbers are:

 

(5, 7) [7 – 5 = 2]

(11, 13) [13 – 11 = 2]

(17, 19) [19 – 17 = 2]

(29, 31) [31 – 29 = 2]

(41, 43) [43 – 41 = 2]

(59, 61) [61 – 59 = 2]

(71, 73) [73 – 71 = 2]