# Perfect Number

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A **Perfect Number** is one for which the sum of its factors (excluding the number itself) is equal to the number itself.

**Examples**:

The first perfect number is 6:

- the factors of 6 are 1, 2, 3 and 6.
- the sum of 1 + 2 + 3 = 6

The second perfect number is 28:

- the factors of 28 are 1, 2, 4, 7, 14 and 28
- the sum of 1 + 2 + 4 + 7 + 14 = 28

The next perfect number is 496:

- the factors are : 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
- the sum of 1 + 2 + 4 + 8 + 16+ 31 + 62 + 124 + 248 = 496

It is relatively straightforward to show that any number P of the form P = 2^{n-1} (2^{n}-1)

for which (2^{n}-1) is prime, is a perfect number.