Prime Numbers

A natural number greater than 1, having only two factors namely 1 and the number itself, is called a prime number

The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ... 

Smallest Prime Number

The smallest prime number   is 2. To be prime, a number must be divisible only by 1 and the number itself which is fulfilled by the number 2

Twin Primes

A pair of prime numbers whose difference is 2, is called twin primes.

For example, (5, 7) is a twin prime pair as is (17,19)

If three successive prime numbers differ by 2, then the prime numbers form a prime triplet. The only prime triplet is (3, 5, 7).

 Express 42 and 100 as the sum of two consecutive primes.

 42 = 19+23

100 = 47+53

Express 31 and 55 as the sum of any three odd primes. 

 31 = 5+7+19

55 = 3 + 23+29

Finding the Prime Numbers by Sieve of Eratosthenes Method

Sieve of Eratosthenes, is a simple method of elimination by which we can easily find the prime numbers upto a given number. This method given by a Greek Mathematician, Eratosthenes of Alexandria, follows some simple steps which are listed below, by which we can find the prime numbers.

 

Step 1: Write the numbers 1 to 100 in ten rows.

Step 2: Cross out 1 because 1 is not a prime.

Step 3: Circle 2 and cross out all multiples of 2. (2, 4, 6, 8, 10, ...)

Step 4: Circle 3 and cross out all multiples of 3. (3, 6, 9, 12, 15, ...)

Step 5: Circle 5 and cross out all multiples of 5. (5, 10, 15, 20, ...)

Step 6: Circle 7 and cross out all multiples of 7. (7, 14, 21, 28, ...)