Statements (71)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:application |
in cryptography and computer science.
|
| gptkbp:are |
numbers that are equal to the sum of their proper divisors
|
| gptkbp:conjecture |
the existence of odd perfect numbers.
|
| gptkbp:connects |
number theory
|
| gptkbp:defines |
a positive integer that is equal to the sum of its proper positive divisors, excluding itself.
|
| gptkbp:discovered_by |
ancient Greek mathematicians.
|
| gptkbp:euclid's_theorem |
if 2^p -1 is prime, then 2^(p-1)(2^p -1) is perfect.
|
| gptkbp:even_perfect_numbers |
all known perfect numbers are even.
|
| gptkbp:example |
6, 28, 496, 8128, 33550336.
|
| gptkbp:first_known_example |
gptkb:6
|
| gptkbp:first_known_example_year |
circa 300 AD
|
| gptkbp:has_implications_for |
in various branches of mathematics.
|
| gptkbp:has_limitations |
no odd perfect numbers have been found.
|
| gptkbp:has_property |
they are always even.
|
| gptkbp:historical_research |
studied by mathematicians like Euclid and Euler.
|
| gptkbp:historical_significance |
in the development of number theory.
|
| https://www.w3.org/2000/01/rdf-schema#label |
perfect numbers
|
| gptkbp:is_explored_in |
modern mathematicians.
|
| gptkbp:is_studied_in |
has implications in algebra.
has implications in analysis. has implications in combinatorics. has implications in computational mathematics. has implications in geometry. has implications in logic. has implications in mathematical aesthetics. has implications in mathematical anthropology. has implications in mathematical architecture. has implications in mathematical art. has implications in mathematical biology. has implications in mathematical communication. has implications in mathematical culture. has implications in mathematical design. has implications in mathematical economics. has implications in mathematical education. has implications in mathematical entrepreneurship. has implications in mathematical ethics. has implications in mathematical finance. has implications in mathematical history. has implications in mathematical innovation. has implications in mathematical linguistics. has implications in mathematical literature. has implications in mathematical logic. has implications in mathematical modeling. has implications in mathematical music. has implications in mathematical philosophy. has implications in mathematical physics. has implications in mathematical policy. has implications in mathematical psychology. has implications in mathematical sociology. has implications in mathematical statistics. has implications in mathematical technology. has implications in numerical analysis. has implications in set theory. has implications in topology. |
| gptkbp:mathematical_properties |
they are related to the divisors of integers.
|
| gptkbp:mathematical_research |
continues to this day.
|
| gptkbp:mathematical_significance |
important in the study of number theory.
|
| gptkbp:notable_examples |
6, 28, 496.
|
| gptkbp:odd_perfect_numbers |
no known odd perfect numbers exist.
|
| gptkbp:related_concept |
abundant numbers
deficient numbers |
| gptkbp:related_to |
gptkb:Mersenne_primes
amicable numbers. sociable numbers. |
| gptkbp:relationship_with |
Fermat's Last Theorem.
|
| gptkbp:sum_of_divisors_function |
related to the σ(n) function.
|
| gptkbp:theory |
related to the distribution of prime numbers.
|
| gptkbp:used_in |
various mathematical proofs.
|
| gptkbp:bfsParent |
gptkb:Matar_Prime
|
| gptkbp:bfsLayer |
6
|