26 lines
1.2 KiB
Plaintext
26 lines
1.2 KiB
Plaintext
[[category:Discrete math]]
|
||
{{task|Prime Numbers}}
|
||
{{task|Numbers}}
|
||
Write a function which says whether a number is perfect.
|
||
|
||
<br>
|
||
[[wp:Perfect_numbers|A perfect number]] is a positive integer that is the sum of its proper 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).
|
||
|
||
|
||
Note: The faster [[Lucas-Lehmer test]] is used to find primes of the form <big> 2<sup>''n''</sup>-1</big>, all ''known'' perfect numbers can be derived from these primes
|
||
using the formula <big> (2<sup>''n''</sup> - 1) × 2<sup>''n'' - 1</sup></big>.
|
||
|
||
It is not known if there are any odd perfect numbers (any that exist are larger than <big>10<sup>2000</sup></big>).
|
||
|
||
The number of ''known'' perfect numbers is '''51''' (as of December, 2018), and the largest known perfect number contains '''49,724,095''' decimal digits.
|
||
|
||
|
||
;See also:
|
||
:* [[Rational Arithmetic]]
|
||
:* [[oeis:A000396|Perfect numbers on OEIS]]
|
||
:* [http://www.oddperfect.org/ Odd Perfect] showing the current status of bounds on odd perfect numbers.
|
||
<br><br>
|
||
|