Perfect Numbers

History:
The term was first coined by Pythagoreans. The greeks thought these numbers have mystical good powers and held them to be "good" numbers. Some biblical scholars considered 6 as a perfect number because they believed that the GOD created the world in six days and GOD's work must be perfect.

Definition:
A positive integer is a perfect number if the sum of its proper factors equals n.
First perfect number is 6 then 28 then 496........

Information:
Based on assumptions, Mathematicians of Middle Ages described:
1.There is a perfect number between any two consecutive powers of 10.
2.Perfect numbers end alternatively in 6 and 8.

Now first 6 perfect numbers are:
1.6
2.28
3.496
4.8128
5.33550336
6.8589869056

Which show both assumptions get wrong as there are no prime numbers of length of 5 digits and 5th and 6th prime numbers though end in 6 but not alternatively in 6 and 8.

For perfect numbers,
Euclid gave a formula for perfect numbers:

" If n is an integer >1 such that 2ⁿ -1 is prime, then N=2^n-1(2ⁿ-1) is a perfect number."

Which gives perfect numbers but there is a fact that no odd perfect numbers are found and there is no proof available stating that odd numbers can not be perfect.