Introduction to practice prime number

Introduction to practice prime number:

To Practice perfect number, we have to know the perfect number. Perfect number is obtained by adding all possible factors of this number, excepted itself but it includes 1.In other words, the addition result of factors is equal to the perfect number. The factor of the perfect number is called proper divisor. The perfect number is denoted as,

N=s(n)

Where,

N denotes perfect number.

S(n) denotes sum of all possible factors.
Types of Perfect Number to Practice:

Perfect number is classified into two different types. They are

Even perfect number
Odd perfect number

Even perfect number:

Even perfect number is invented by Euclid. The formula to practice even perfect number is 2p-1(2p-1). Where p denotes prime number.

Example to practice even perfect number:

When p=1: 21-1 ( 21 – 1) = 20 (21 – 1 ) = 1 ( 2 – 1 ) = 1 ( 1 ) = 1

When p=2: 22-1 ( 22 – 1) = 21 (22 – 1 ) = 2 ( 4 – 1 ) = 2 ( 3 ) = 6

When p=3: 23-1 ( 23 – 1) = 22 (23 – 1 ) = 4 ( 8 – 1 ) = 4 ( 7 ) = 28

When p=4: 24-1 ( 24 – 1) = 23 (24 – 1 ) = 8 ( 16 – 1 ) = 8 ( 15 ) = 120

When p=5: 25-1 ( 25 – 1) = 24 (25 – 1 ) = 16 ( 32 – 1 ) = 16 ( 31 ) = 496

Odd perfect number:

Euclid invented the perfect number, but he stated that there is no odd perfect number. But Euler took care on this. Up to this odd perfect number is unknown. If there is any perfect number that should satisfy

N>10300

Where N is in the form of,

N =qa p2ek 1 …..p2ekk
Where
q,p1......pk  denotes distinct prime numbers ( defined by Euler)
q=a=1 ( by Euler)
The least prime factor to N is smaller that (2k + 8) / 3

qa =1020
N < 24k+1
The most prime factor of  N is larger that 108
The second prime factor is greater that 104

Example to Practice of Perfect Number:

The perfect number is 6.

1 + 2 + 3 = 6

Where 1,2 and 3 are proper divisor. When we add these proper divisor or factor we will get perfect number.