Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:all_known_perfect_numbers |
are even
|
| gptkbp:defines |
A perfect number that is even
|
| gptkbp:discoveredBy |
gptkb:Euclid
|
| gptkbp:example |
6
|
| gptkbp:form |
2^(p-1) × (2^p − 1) where 2^p − 1 is prime
|
| gptkbp:fourth_example |
8128
|
| https://www.w3.org/2000/01/rdf-schema#label |
even perfect numbers
|
| gptkbp:property |
triangular number
the sum of the reciprocals of the divisors equals 2 abundant number ends with 6 or 28 alternately equal to the sum of their proper divisors harmonic divisor number if 2^p − 1 is prime, then p is also prime number of divisors is a power of 2 all even perfect numbers are congruent to 6 mod 12 except 6 related to binary representations the largest known perfect numbers are even |
| gptkbp:relatedTo |
gptkb:Mersenne_primes
|
| gptkbp:second_example |
28
|
| gptkbp:sequence |
6, 28, 496, 8128, 33550336, ...
|
| gptkbp:studiedBy |
gptkb:Euler
|
| gptkbp:third_example |
496
|
| gptkbp:unknown_property |
existence of odd perfect numbers is unknown
|
| gptkbp:bfsParent |
gptkb:Euclid–Euler_theorem
|
| gptkbp:bfsLayer |
8
|