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).
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, ...)
