*A perfect number is a number whose proper factors sum to itself. For example:*

*6 has a proper factors of 1, 2 and 3 and 1 + 2 + 3 = 6 so 6 is a perfect number.*

*Produce a program to find the first three perfect numbers.*

`<?`

` // the amount of perfect numbers to find`

` // the 4th perfect number is over 8 thousand, which takes 17 seconds to find on my machine`

` // the 5th perfect number is over 3 million, so don't try finding that!`

` $perfect_needed = 3;`

` `

` // start testing at one`

` $current = 1;`

` // only loop while not enough have been found`

` while (count($perfect_numbers) < $perfect_needed)`

` {`

` // reset the total to zero`

` $total = 0;`

` // loop from 1 to the current number being tested`

` // the number to test up to only needs to be half the current amount `

` for ($n = 1; $n < intval($current / 2)+1; $n++)`

` {`

` // check if the nested loop counter divides into the current number perfectly`

` if ($current % $n == 0)`

` // if so, add it to the current total`

` $total += $n;`

` }`

` // if the total is the same amount as the number being tested, it's a perfect number`

` if ($total == $current)`

` // add it to the array of perfect numbers`

` $perfect_numbers[] = $current;`

` `

` // test the next number`

` $current++;`

` } `

` // show how many perfect numbers were being found and output them`

` echo 'The first ' . $perfect_needed . ' perfect numbers are: ' . implode(', ', $perfect_numbers);`

`?>`

Which produces:

The first 3 perfect numbers are: 6, 28, 496

- Feb 4, 2005 - Added solution 1.

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