Prime numbers in Mathematics have a great property that they are divisible ONLY by '1' and by itself.
Traditional method to check whether a given number is prime number or not:
Check for the divisibility test for each and every number from 1-number but that is the worst strategy to solve problems based on prime numbers in aptitude.
Moderate method suggested to check for the Divisibility test for each and every prime or odd number from 1 to √(number) and this reduced some complexity in solving these problems.
Even this method failed to minimize the computation and thus a great concept of Prime Series came into existence which generalized the form of a prime number.
Generalized form of Prime number: 6K ± 1 (K is a natural number)
"Every prime number is in the form of 6K ± 1 " but not every 6K ± 1 is Prime number.
To prove the above statement,
We can define each and every integer as (6k-3) : Divisible by 3
(6k-2) : Divisible by 2
(6k+0) : Divisible by 6
(6k+2) : Divisible by 2
The terms which are left are 6k+1 and 6*k-1 so prime numbers will definitely lie in this area.
This technique helps you in eliminating the options and processing the answer more efficiently in less time.
Prime numbers upto 100 are : 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.
There is no algebraic equation which fits all the prime numbers.
There are 15 prime numbers between 0 and 50
There are 25 prime numbers between 0 and 100
There are 21 prime numbers between 100 and 200.
There are 95 prime numbers between 0 and 500.
There are 168 prime numbers between 0 and 1000.
Prime numbers keeps reducing with its range. 0-100, 100-200 (100-200 will have less number of primes than 0-100)