Perfect number properties||Even perfect number||Perfect number concept||Condition||Mersenne primes.

Описание: Perfect number properties||Even perfect number||Perfect number concept||Condition||Mersenne primes.

Perfect numbers were thought to have mystical healing properties and were even used to illustrate the existence of Creator. This video is about those mystical numbers that is called perfect number. Example of perfect numbers are 6,28,496,8128.....What is a perfect number and even perfect number? How to find perfect numbers? What is a Mersenne prime number? The answer of this type of many questions are discussed in this video. Also discussion about the perfect number condition and perfect number concept with examples.Perfect number is a positive integer that is equal to the sum of its proper divisors.A perfect number is a positive integer that is half of the sum of its positive divisors, including the number itself. The following theorems related to perfect number also discussed in this video.
Euclid’s Theorem: If 2^p - 1 is a prime number then 2^(p-1) (2^p -1) is a perfect number.
Mersenne Prime: Prime numbers of the form 2^p - 1 are known as Mersenne.
Euler’s Theorem: If n is an even perfect number, then it is of the form n=2^(p-1) (2^p -1) where p is prime and 2^p - 1 is Mersenne prime.
The Sigma Function: Sigma(n)=the sum of all unique divisors of n including 1 and n.
Theorem: Every even perfect number greater than 6 can be expressed as the sum of the cubes of consecutive odd integers.
Some discussion about the odd prime number that is finding an odd perfect number or to prove that there is no such thing as an odd perfect number.

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