Perfect numbers: Difference between revisions
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[[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). |
[[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). |
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Note: The faster [[Lucas-Lehmer test]] is used to find primes of the form 2<sup>''n''</sup>-1, all ''known'' perfect numbers can be derived from these primes using the formula (2<sup>''n''</sup> - 1) × 2<sup>''n'' - 1</sup>. It is not known if there are any odd perfect numbers. |
Note: The faster [[Lucas-Lehmer test]] is used to find primes of the form 2<sup>''n''</sup>-1, all ''known'' perfect numbers can be derived from these primes using the formula (2<sup>''n''</sup> - 1) × 2<sup>''n'' - 1</sup>. It is not known if there are any odd perfect numbers (any that exist are larger than 10<sup>2000</sup>). |
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'''See also''' |
'''See also''' |
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* [[Rational Arithmetic]] |
* [[Rational Arithmetic]] |
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*[[oeis:A000396|Perfect numbers on OEIS]] |
* [[oeis:A000396|Perfect numbers on OEIS]] |
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* [http://www.oddperfect.org/ Odd Perfect] showing the current status of bounds on odd perfect numbers. |
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=={{header|Ada}}== |
=={{header|Ada}}== |
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