Perfect number checker
Check whether a number is perfect — meaning it equals the sum of all its proper divisors (excluding itself).
Number
What is a perfect number?
A perfect number equals the sum of its proper divisors. 6 = 1+2+3. 28 = 1+2+4+7+14. 496 = 1+2+4+8+16+31+62+124+248.
Known perfect numbers
Only 51 perfect numbers are known: 6, 28, 496, 8128, 33550336, ... All known perfect numbers are even. Whether an odd perfect number exists is unknown.
Euclid-Euler theorem
An even number is perfect if and only if it has the form 2^(p−1) × (2^p − 1) where 2^p − 1 is a Mersenne prime.
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