## What are the applications of perfect number?

The primes are a good example. After noticing the primes then one can show the prime factorization theorem. Primes can be used to design a cryptographical system (RSA) powerful enough to protect many financial transactions at the current time. Perfect numbers create a “playground” for the interested.

### How do you work out the perfect number?

A number is perfect if the sum of its proper factors is equal to the number. To find the proper factors of a number, write down all numbers that divide the number with the exception of the number itself. If the sum of the factors is equal to 18, then 18 is a perfect number.

What is perfect number example?

Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.

Are perfect numbers important?

Perfect numbers were deemed to have important numerological properties by the ancients, and were extensively studied by the Greeks, including Euclid. In a posthumous 1849 paper, Euler provided the first proof that Euclid’s construction gives all possible even perfect numbers (Dickson 2005, p. 19).

## What is the 6th perfect number?

List of perfect numbers

Rank p Perfect number
6 17 8589869056
7 19 137438691328
8 31 2305843008139952128
9 61 265845599156…615953842176

### Is 8128 a perfect number Class 6?

Yes, 8128 is a perfect number, that is to day 8128 equals the sum of its proper positive divisors, i.e., the sum of its divisors excluding 8128 itself. Note that perfect numbers are very rare: there are only 4 perfect numbers smaller than 1 000 000, viz., 6, 28, 496 and 8 128.

Why is 10 not a perfect number?

Note that 10 is not an aliquot part of 10 since it is not a proper quotient, i.e. a quotient different from the number itself. A perfect number is defined to be one which is equal to the sum of its aliquot parts.

What is the 100th perfect number?

There are only 2 perfect numbers from 1 to 100 which are 6 and 28.

## Are there any real applications of perfect numbers?

But for perfect numbers the best I could find is: The earth was created in 6 days by God because 6 is perfect. Also, the cycle of the moon is 28 days. ( 3) This page ( http://www-history.mcs.st-andrews.ac.uk/HistTopics/Perfect_numbers.html) has a lot of history but no real applications.

### Which is the formula for a perfect number?

A Perfect Number “n”, is a positive integer which is equal to the sum of its factors, excluding “n” itself. Euclid, over two thousand years ago, showed that all even perfect numbers can be represented by, N = 2 p-1(2 p -1) where p is a prime for which 2 p -1 is a Mersenne prime.

When do you have an even perfect number?

N = 2p-1(2p -1) where p is a prime for which 2p -1 is a Mersenne prime. That is, we have an even Perfect Number of the form N whenever the Mersenne Number 2 p -1 is a prime number.

Which is the smallest perfect number in the world?

The smallest perfect number is 6, which is the sum of 1, 2, and 3. How Many Perfect Numbers are there and What are the Perfect Numbers from 1 to 100? There are around 51 known perfect numbers. There are only 2 perfect numbers from 1 to 100 which are 6 and 28.

What are the applications of perfect number? The primes are a good example. After noticing the primes then one can show the prime factorization theorem. Primes can be used to design a cryptographical system (RSA) powerful enough to protect many financial transactions at the current time. Perfect numbers create a “playground” for the interested. How…