Final+Essay

= Do not forget your vivencias, please ! ! So far 5pts = =**The perfect number**=

"In mathematics, a perfect number is a positive integer that is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself), or σ(N) = 2n." (wikipedia).


 * Source: Wikipedia (pon el enlace) **

This numbers have were discovered by Euclid. So far, there are only 39 perfect numbers discovered: the first four are 6,28, 496, 8128. and the formula to get them is: where n are a prime number. For example if n=2 then 2^(2-1)x(2^2-1)=2^1x3=6 and 6 is a perfect number because it is the sum of his divisors 6=3+2+1.

Euler add **ed** some important information to this equation and is that 2^n-1 will always throw as a result a prime number so, the perfect numbers are relative to prime numbers.

A singular observation about the perfect numbers is that there are no any odd perfect numbers, at least not discovered, yet. Instead, there are some Hypothesis about __how could be a perfect number__ **how a perfect number could be**, and its characteristics. Of course, there are people who don't believe in the existence of any odd perfect number, their first arguments are in the formula of perfect numbers because 2^x will be always a even number and every even number multiplied by another even number or a odd number is equal to another even number. But this don' t stop some mathematicians, and they are searching some characteristics about how should be the first odd perfect number. Some of that are that it should be bigger that 10^300 and should have at least 8 prime numbers as factors.

In my personal opinion **comma** this odd perfect number exists. First, if the characteristic exists the number must exist__s__, second, and speaking by myself, there __are__ **is** not __any__ **a** sequence of number **s** that are completely odd or completely even __by__ **for** example the sequence of the prime numbers, they are almost all odd, except by the number 2, it means there __are__ **is** at least one even number, so, if perfect numbers are relative of prime number, then __it__ **there** must **be** __exist__ at least 1 odd perfect number. Another reason for me to believe in that __are that the equation itself no have all the prime numbers on his domain.__ **confusing**