Some learning points about prime

Prime Numbers:

A natural number larger than unity is a prime number if it 
does not have other divisors except for itself and unity.
Note:-Unity i e,1 is not a prime number.

Properties Of Prime Numbers:

->The lowest prime number is 2.
->2 is also the only even prime number.
->The lowest odd prime number is 3.
->The remainder when a prime number p>=5 is divided by 6 is 1 or 5.However, 
if a number on being divided by 6 gives a remainder 1 or 5 need not be 
prime....so, p = 6k+1 or 6k+5
->The remainder of division of the square of a prime number p>=5 divide by 
24 is 1.....p^2 = 24k+1
->For prime numbers p>3, p²-1 is divided by 24.
->If a and b are any 2 odd primes then a²-b² is composite. Also a²+b² 
is composite.
->The remainder of the division of the square of a prime number p>=5
divided by 12 is 1....p^2 = 12k + 1

Process to Check A Number s Prime or not:

Take the square root of the number.
Round of the square root to the next highest integer call this number as Z.
Check for divisibility of the number N by all prime numbers below Z. If 
there is no numbers below the value of Z which divides N then the number
will be prime.

Example 239 is prime or not?
√239 lies between 15 or 16.Hence take the value of Z=16.
Prime numbers less than 16 are 2,3,5,7,11 and 13.
239 is not divisible by any of these. Hence we can conclude that 239 
is a prime number.

Learn
n-->Number    pn--->number of primes less than n
n              pn
10            4
50          14
100        24
Sum of 1st 9 primes = 100